[Yuima-commits] r195 - pkg/yuimadocs/inst/doc/JSS
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Fri Nov 11 20:48:24 CET 2011
Author: iacus
Date: 2011-11-11 20:48:23 +0100 (Fri, 11 Nov 2011)
New Revision: 195
Modified:
pkg/yuimadocs/inst/doc/JSS/article.Rnw
pkg/yuimadocs/inst/doc/JSS/bibliography.bib
Log:
update
Modified: pkg/yuimadocs/inst/doc/JSS/article.Rnw
===================================================================
--- pkg/yuimadocs/inst/doc/JSS/article.Rnw 2011-10-18 07:45:17 UTC (rev 194)
+++ pkg/yuimadocs/inst/doc/JSS/article.Rnw 2011-11-11 19:48:23 UTC (rev 195)
@@ -9,6 +9,8 @@
\usepackage{amsmath,amssymb}
+\usepackage[utf8x]{inputenc}
+
%% almost as usual
\author{Alexandre Brouste\\University of Le Mans \And
Masaaki Fukasawa\\Osaka University\And
@@ -81,7 +83,7 @@
%% preamble for Rnw files
<<print=FALSE, echo=FALSE>>=
options(prompt="R> ")
-options(width=70)
+options(width=60)
@
\def\ve{{\varepsilon}}
@@ -110,12 +112,12 @@
\section{Introduction}
-The plan of the YUIMA Project is to define the bases for a complete environment for simulation and inference for stochastic processes via an \proglang{R} package called \pkg{yuima}.
+The plan of the YUIMA Project is to define the bases for a complete environment for simulation and inference for stochastic processes via an \proglang{R} \citep{ERRE} package called \pkg{yuima}.
The package \pkg{yuima} provides
an object-oriented programming environment
for simulation and statistical inference
for stochastic processes by \proglang{R}.
-The \pkg{yuima} package adopts the \texttt{S4} system of classes and methods \citep{chambers98}.
+The \pkg{yuima} package adopts the S4 system of classes and methods \citep{chambers98}.
Under this framework,
the \pkg{yuima} package also supplies various functions
@@ -166,22 +168,22 @@
Although we assume that the reader of this paper has a basic knowledge of the \proglang{R} language, most of the examples are easy to be understood by anyone.
-\section{The \pkg{yuima} package}\label{sec2}
-The package \pkg{yuima} depends on some other packages, like \pkg{zoo}, which can be installed separately.
+\section{The \pkg{yuima} Package}\label{sec2}
+The package \pkg{yuima} depends on some other packages, like \pkg{zoo} \citep{zoo}, which can be installed separately.
The package \pkg{zoo} is used internally to store time series data. This dependence may change in the future adopting a more flexible class for internal storage of time series.
-\subsection{How to obtain the package}
-The \pkg{yuima} package is hosted on \textsf{R-Forge} and the web page
+\subsection{How to Obtain the Package}
+The \pkg{yuima} package is hosted on R-Forge and the web page
of the Project is \url{http://r-forge.r-project.org/projects/yuima}.
-The \textsf{R-Forge} page contains the latest development version, and stable
-version of the package will also be available through \textsf{CRAN}.
+The R-Forge page contains the latest development version, and stable
+version of the package will also be available through CRAN.
Development versions of the package are not supposed to be stable or functional, thus
the occasional user should consider to install the stable version first.
-The package can be installed from \textsf{R-Forge} using
+The package can be installed from R-Forge using
\code{install.packages("yuima",repos="http://R-Forge.R-project.org")}.
-\subsection{The main object and classes}
+\subsection{The Main Object and Classes}
Before discussing the methods for simulation and inference for stochastic processes solutions to stochastic differential equations, here we discuss the main classes in the package.
As mentioned there are different classes of objects defined in the \pkg{yuima} package and
the main class is called the \code{yuima-class}. This class is composed of several slots.
@@ -196,7 +198,7 @@
-\subsection{The $\tt yuima.model$ class}
+\subsection{The \code{yuima.model} Class}
At present, in \pkg{yuima} three main classes of stochastic differential equations can be easily specified. All multidimensional and eventually as parametric models.
\begin{itemize}
\item diffusions $\displaystyle \de X_t=a(t,X_t)dt + b(t,X_t)\de W_t $, where $W_t$ is a standard Brownian motion;
@@ -250,7 +252,7 @@
name of the solution variable (left-hand-side) of each equation in the model, in the corresponding order.
\item \code{noise.number} indicates the number of sources of noise.
\item \code{xinit} initial value of the stochastic differential equation;
-\item \code{equation.number} represents the number of equations, i.e. the number of one dimensional
+\item \code{equation.number} represents the number of equations, i.e., the number of one dimensional
stochastic differential equations.
\item \code{dimension} reports the dimensions of the parameter space. It is a list of the
same length of \code{parameter} with the same names.
@@ -258,10 +260,10 @@
\end{itemize}
As seen in the above, the parameter space is accurately described internally in a \code{yuima} object because in inference for stochastic differential equations, estimators of different parameters have different properties. Usually, the rate of convergence for estimators in the diffusion coefficient are similar to the ones in the i.i.d. sampling while estimators of parameters in the drift coefficient are slower or, in some cases, not even consistent. The \pkg{yuima} always tries to implement the best statistical inference for the given model under the observed sampling scheme.
-\section{Model specification}\label{sec3}
+\section{Model Specification}\label{sec3}
In order to show how general is the approach in the \pkg{yuima} package we present some examples.
-\subsection{Diffusion processes}
+\subsection{Diffusion Processes}
Assume that we want to describe the following stochastic differential equation
$$\de X_t = -3 X_t \de t + \frac{1}{1+X_t^2}\de W_t$$
This is done in \pkg{yuima} specifying the drift and diffusion coefficients as plain mathematical expressions
@@ -272,11 +274,9 @@
mod1 <- setModel(drift = "-3*x", diffusion = "1/(1+x^2)")
@
At this point, the package fills the proper slots of the \code{yuima} object
-{\scriptsize
<<>>=
str(mod1)
@
-}
For the above, it is possible to see that the jump coefficient is void and the Hurst parameter is set to 0.5, because this corresponds to the standard Brownian motion.
Now, with \code{mod1} in hands, it is very easy to simulate a trajectory of the process as follows
@@ -288,24 +288,20 @@
\noindent
The \code{simulate} function fills in addition the two slots \code{data} and \code{sampling} of the \code{yuima} object.
-{\scriptsize
<<>>=
str(X,vec.len=2)
@
-}
-\subsection{Specification of parametric models}
+\subsection{Specification of Parametric Models}
When a parametric model like
$$\de X_t = -\theta X_t \de t + \frac{1}{1+X_t^\gamma}\de W_t$$
is specified, \pkg{yuima} attempts to distinguish the parameters' names from the ones of the state and time variables
<<echo=TRUE, print=FALSE,results=hide>>=
mod2 <- setModel(drift = "-theta*x", diffusion = "1/(1+x^gamma)")
@
-{\scriptsize
<<>>=
str(mod2)
@
-}
In order to simulate the parametric model it is necessary to specify the values of the parameters as the next code shows
<<echo=TRUE, print=FALSE,fig=TRUE,height=4,results=hide>>=
set.seed(123)
@@ -313,7 +309,7 @@
plot(X)
@
-\subsection{Multidimensional processes}
+\subsection{Multidimensional Processes}
Next is an example with two stochastic differential equations driven by three independent Brownian motions
$$
\begin{aligned}
@@ -352,7 +348,7 @@
$$
where $g(t) = 0.4 + (0.1 + 0.2t) e^{-2t}$.
-\subsubsection{Fractional Gaussian noise}
+\subsubsection{Fractional Gaussian Noise}
In order to specify a stochastic differential equation driven by fractional Gaussian noise it is necessary to specify the value of the Hurst parameter. For example, if we want to specify the following model
$$\de Y_t = 3 Y_t \de t + \de W_t^H$$
we proceed as follows
@@ -366,21 +362,19 @@
\noindent
In this case, the appropriate slot is now filled
@
-{\scriptsize
<<>>=
str(mod4)
@
-}
The user can choose between the two simulation schemes, namely the Cholesky method and \citet{WoodChan} method.
-\subsection{L\'evy processes}
+\subsection{L\'evy Processes}
Jump processes can be specified in different ways in mathematics and hence in \pkg{yuima} package.
-Let $Z_t$ be a Compound Poisson Process (i.e. jumps size follow some distribution, like the Gaussian law and jumps occur at Poisson times).
+Let $Z_t$ be a Compound Poisson Process (i.e., jumps size follow some distribution, like the Gaussian law and jumps occur at Poisson times).
Then it is possible to consider the following SDE which involves jumps
$$\de X_t = a(X_t)\de t + b(X_t)\de W_t + \de Z_t$$
In the next example we consider a compound Poisson process with intensity $\lambda=10$ with Gaussian jumps.
This model can be specified in \code{setModel} using the argument \code{measure.type="CP"}
-A simple Ornstein-Uhlembeck process with Gaussian jumps
+A simple Ornstein-Uhlenbeck process with Gaussian jumps
$$\de X_t = -\theta X_t \de t + \sigma \de W_t + \de Z_t$$
is specified as
<<echo=TRUE, print=FALSE,fig=TRUE,width=9,height=4,results=hide>>=
@@ -393,7 +387,7 @@
@
\noindent
-Another possibility is to specify the jump component via the L\'evy measure. Without going into too much details, here is an example of specification of a simple Ornstein-Uhlembeck process with IG (Inverse Gaussian) L\'evy measure
+Another possibility is to specify the jump component via the L\'evy measure. Without going into too much details, here is an example of specification of a simple Ornstein-Uhlenbeck process with IG (Inverse Gaussian) L\'evy measure
$$\de X_t = -x \de t + \de Z_t$$
<<echo=TRUE, print=FALSE,fig=TRUE,width=9,height=4,results=hide>>=
mod6 <- setModel(drift="-x", xinit=1, jump.coeff="1",
@@ -403,7 +397,7 @@
plot(X)
@
-\subsection{Specification of generic models}
+\subsection{Specification of Generic Models}
In general, the \pkg{yuima} package allows to specify a large family of models solutions to
$$\de X_t =a(X_t)\de t + b(X_t)\de W_t + c(X_t)\de Z_t$$
using the following interface
@@ -416,7 +410,7 @@
\code{rIG} (Inverse Gaussian), \code{rNIG} (Normal Inverse Gaussian), \code{rbgamma} (Bilateral Gamma), \code{rngamma} (Normal Gamma) and \texttt{rstable} (Stable Laws).
Other user-defined RNG can be used freely.
-\subsection{Simulation, sampling and subsampling}
+\subsection{Simulation, Sampling and Subsampling}
The \code{simulate} function simulates \code{yuima} models according to Euler-Maruyama scheme in the presence of non-fractional diffusion noise and L\'evy jumps and uses the Cholesky or the Wood and Chan methods for the fractional Gaussian noise.
The \code{simulate} function accepts several arguments including the description of the sampling structure, which is an object of type \code{yuima.sampling}. The \code{setSampling} allow for the specification of different sampling parameters including random sampling. Further, the \code{subsampling} allow to subsample a trajectory of a simulated stochastic differential equation or a given time series in the \code{yuima.data} slot of a \code{yuima} object.
Sampling and subsampling can be specified jointly as arguments to the \code{simulate} function. This is convenient if one wants to simulate data at very high frequency but then return only low frequency data for inference or other applications. We now go through few examples just to describe the use of standard arguments to these functions but the reader is invited to go thorough the man pages of the \code{yuima} packages for complete details.
@@ -500,10 +494,10 @@
-\section{Asymptotic expansion}\label{sec4}
+\section{Asymptotic Expansion}\label{sec4}
The \pkg{yuima} package can handle asymptotic expansion of functionals of $d$-dimensional diffusion process
$$\de X_t^\ve = a(X_t^\ve,\ve)\de t + b(X_t^\ve,\ve)\de W_t, \qquad \ve \in(0,1]$$
-with $W_t$ and $r$-dimensional Wiener process, i.e. $W_t=(W_t^1, \ldots, W_t^r)$.
+with $W_t$ and $r$-dimensional Wiener process, i.e., $W_t=(W_t^1, \ldots, W_t^r)$.
The functional is expressed in the following abstract form
\begin{equation}
\label{yuima:func1}
@@ -548,7 +542,7 @@
<<echo=TRUE, print=FALSE>>=
str(yuima at functional)
@
-Then, to obtain the first term in the asymptotic expansion (i.e. for $\ve=0$), it is as easy as calling the function \code{F0} on the \code{yuima} object:
+Then, to obtain the first term in the asymptotic expansion (i.e., for $\ve=0$), it is as easy as calling the function \code{F0} on the \code{yuima} object:
<<echo=TRUE, print=FALSE>>=
F0 <- F0(yuima)
F0
@@ -575,11 +569,11 @@
-\section{Inference for stochastic processes}\label{sec5}
+\section{Inference for Stochastic Processes}\label{sec5}
The \pkg{yuima} implements several optimal techniques for parametric, semi- and non-parametric estimation of (multidimensional) stochastic differential equations.
Although most of the examples in this section are given on simulated data, the main way to fill up the \code{data} slot of a \code{yuima} object is to use the function \code{setYuima}. The function \code{setYuima} sets various slots of the \code{yuima} object. In particular, to estimate a \code{yuima.model} called \code{mod} on the data \code{X} one can use a code like this \code{my.yuima <- setYuima(data=setData(X), model=mod)} and then pass \code{my.yuima} to the inference functions as described in what follows.
-\subsection{Quasi Maximum Likelihood estimation}
+\subsection{Quasi Maximum Likelihood Estimation}
Consider the multidimensional diffusion process
$$
\de X_t = b(\theta_2,X_t)\de t + \sigma(\theta_1, X_t) \de W_t
@@ -594,7 +588,7 @@
+\frac{1}{\Delta_n}
\Sigma_{i-1}^{-1}(\theta_1)[\Delta X_i-\Delta_n b_{i-1}(\theta_2)]^{\otimes 2}\right\}
\end{eqnarray}}
-where $\theta=(\theta_1, \theta_2)$, $\Delta X_i=X_{t_i}-X_{t_{i-1}}$, $\Sigma_i(\theta_1)=\Sigma(\theta_1,X_{t_i})$, $b_i(\theta_2)=b(\theta_2,X_{t_i})$, $\Sigma=\sigma^{\otimes 2}$, $A^{\otimes 2}= A^T A$ and $A^{-1}$ the inverse of $A$, $A[B]^{\otimes 2} = B^T A B$. Then, \citep[see e.g.][]{Yoshida92, Kessler97}, the QML estimator of $\theta$ is
+where $\theta=(\theta_1, \theta_2)$, $\Delta X_i=X_{t_i}-X_{t_{i-1}}$, $\Sigma_i(\theta_1)=\Sigma(\theta_1,X_{t_i})$, $b_i(\theta_2)=b(\theta_2,X_{t_i})$, $\Sigma=\sigma^{\otimes 2}$, $A^{\otimes 2}= A^T A$ and $A^{-1}$ the inverse of $A$, $A[B]^{\otimes 2} = B^T A B$. Then, \citep[see e.g.,][]{Yoshida92, Kessler97}, the QML estimator of $\theta$ is
$$\tilde\theta_n=\arg\min_\theta \ell_n({\bf X}_n,\theta)$$
As an example, we consider the simple model
\begin{equation}
@@ -623,7 +617,7 @@
@
Notice the interface and the output of the \code{qmle} is quite similar to the ones of the standard \code{mle} function of the \pkg{stats4} package of the base \proglang{R} system.
-\subsection{Adaptive Bayes estimation}
+\subsection{Adaptive Bayes Estimation}
Consider again the diffusion process solution to
\begin{equation}
\de X_t=b(X_t,\theta_2)\de t+\sigma(X_t,\theta_1)\de W_t,
@@ -680,7 +674,7 @@
@
%The argument \code{method="nomcmc"} in \code{adaBayes} performs numerical
%integration, otherwise MCMC method is used.
-\subsubsection{Small sample size}
+\subsubsection{Small Sample Size}
It is known from the theory that the estimation of the drift in a diffusion process strongly depend on the length of the observation interval $[0,T]$.
In our example above, we took $T=n^\frac13$, with $n = \Sexpr{n}$, which is approximatively \Sexpr{round(n^(1/3),2)}. Now we reduce the sample size to $n=500$ and the value of $T$ is then $T=\Sexpr{round(500^(1/3),2)}$.
We then apply both quasi-maximum likelihood and adaptive Bayes type estimators to these data
@@ -704,7 +698,7 @@
Compared to the results above, we see that the parameters in the diffusion coefficients are estimated with good quality while for the parameters in the drift the quality of estimation deteriorates. The adaptive Bayes estimator seems to perform a little better though.
-\subsection{Asynchronous covariance estimation}
+\subsection{Asynchronous Covariance Estimation}
Suppose that two It\^o processes are observed
only at discrete times in a nonsynchronous manner.
We are interested in estimating the covariance of the two processes accurately
@@ -769,7 +763,7 @@
tends to $0$.
See \citet{hay-yos05,hay-yos04,hay-yos06,hay-yos08} for details.
-\subsubsection{Example: data generation and estimation by \pkg{yuima} package}
+\subsubsection{Example: Data Generation and Estimation by \pkg{yuima} Package}
We will demonstrate how to apply cce function to
nonsynchronous high-frequency data by simulation.
As an example, consider a two dimensional stochastic process
@@ -898,7 +892,7 @@
plot(Y,main="asynchronous data")
@
-\subsubsection{Asynchronous estimation for nonlinear systems}
+\subsubsection{Asynchronous Estimation for Nonlinear Systems}
Consider now the two-dimensional system with nonlinear feedback
$$
\begin{aligned}
@@ -949,7 +943,7 @@
cce(Y)
@
-\subsection{Change point analysis}
+\subsection{Change-Point Analysis}
Consider a multidimensional stochastic differential equation of the form
$$
\de Y_t = b_t \de t + \sigma(X_t,\theta) \de W_t,\ \ t\in[0,T],
@@ -969,7 +963,7 @@
& \mbox{ for } t\in[\tau^*,T].
\end{array}
$$
-The change point $\tau^*$ instant is unknown and
+The change-point $\tau^*$ instant is unknown and
is to be estimated, along with $\theta_0^*$ and $\theta_1^*$, from the observations sampled
from the path of $(X,Y)$. The \pkg{yuima} implements the quasi-maximum likelihood approach as in \citet{iacyos09} described in the following.
Let $\Delta_iY=Y_{t_i}-Y_{t_{i-1}}$ and
@@ -991,7 +985,7 @@
$\hat{\theta}_k$ for each $\theta_k$, $k=0,1$.
In case $\theta_k^*$ are known, we define $\hat{\theta}_k$
just as $\hat{\theta}_k=\theta_k^*$.
-The change point estimator of $\tau^*$ is
+The change-point estimator of $\tau^*$ is
\begin{eqnarray*}
\hat{\tau}_n&=&\arg\!\!\min\limits_{t\in[0,T]}
\Phi_n(t;\hat{\theta}_0,\hat{\theta}_1).
@@ -1017,8 +1011,8 @@
\de W_t^1\\ \de W_t^2
\end{array}\right)
$$
-where $b_1(\cdot)$ and $b_2(\cdot)$ are any functions and $\theta_{1.k}$ and $\theta_{2.k}$ the value of the parameters before ($k=0$) and after $k=1$) the change point.
-Just for simplicity and in order to simulate some data, we specify some specific form for $b_1(\cdot)$ and $b_2(\cdot)$ but this information will not be used in the change point analysis.
+where $b_1(\cdot)$ and $b_2(\cdot)$ are any functions and $\theta_{1.k}$ and $\theta_{2.k}$ the value of the parameters before ($k=0$) and after $k=1$) the change-point.
+Just for simplicity and in order to simulate some data, we specify some specific form for $b_1(\cdot)$ and $b_2(\cdot)$ but this information will not be used in the change-point analysis.
For example, we will simulate
the following 2-dimensional stochastic differential equation
$$
@@ -1043,7 +1037,7 @@
X^1_0=1.0,\quad
X^2_0=1.0,\quad
$$
-with change point instant at time $\tau=0.4$. First, we describe the model to be simulated
+with change-point instant at time $\tau=0.4$. First, we describe the model to be simulated
<<cpoint1,eval=TRUE, echo=TRUE,results=hide>>=
diff.matrix <- matrix(c("theta1.k*x1","0*x2","0*x1","theta2.k*x2"), 2, 2)
drift.c <- c("sin(x1)", "3-x2")
@@ -1051,7 +1045,7 @@
ymodel <- setModel(drift=drift.matrix, diffusion=diff.matrix, time.variable="t",
state.variable=c("x1", "x2"), solve.variable=c("x1", "x2"))
@
-and then simulate two trajectories. One up to the change point $\tau=4$ with parameters $\theta_{1.0}=0.1$ and $\theta_{2.0}=0.2$
+and then simulate two trajectories. One up to the change-point $\tau=4$ with parameters $\theta_{1.0}=0.1$ and $\theta_{2.0}=0.2$
<<cpoint3,results=hide>>=
n <- 1000
@@ -1090,7 +1084,7 @@
plot(yuima)
@
-As said, the change point analysis do not consider the information coming from the drift part of the model and \pkg{yuima} ignores this internally.
+As said, the change-point analysis do not consider the information coming from the drift part of the model and \pkg{yuima} ignores this internally.
Just to make clear that the information on the drift term is not considered by the function \code{CPoint}, we redefine the \code{yuima} model removing the information coming from the drift and then adding back the data.
<<cpoint4b>>=
noDriftModel <- setModel(drift=c("0", "0"), diffusion=diff.matrix, time.variable="t",
@@ -1105,8 +1099,8 @@
t.est2 <- CPoint(noDriftModel,param1=t0,param2=t1)
t.est2$tau
@
-Now we proceed first with the estimation of the parameters before and after the change point. The \pkg{yuima} package contains two functions
-which are useful in the framework of change point or sequential analysis.
+Now we proceed first with the estimation of the parameters before and after the change-point. The \pkg{yuima} package contains two functions
+which are useful in the framework of change-point or sequential analysis.
The function \code{qmleL} estimates a model by quasi maximum likelihood using observations in the time interval $[0,t]$ where $t$ cam be specificed by the user. In our example, we set \code{t=0.2}. Similary for \code{qmleR}, which uses only observations in the time interval $[t, T]$. In our example, we take \code{t=0.8}.
<<>>=
qmleL(noDriftModel, t=2, start=list(theta1.k=0.1, theta2.k=0.1),lower=list(theta1.k=0, theta2.k=0), upper=list(theta1.k=1, theta2.k=1), method="L-BFGS-B") -> estL
@@ -1114,15 +1108,15 @@
t0.est <- coef(estL)
t1.est <- coef(estR)
@
-and now we proceed with change point estimation
+and now we proceed with change-point estimation
<<>>=
t.est3 <- CPoint(noDriftModel,param1=t0.est,param2=t1.est)
t.est3
@
-Notice that, even if the estimated parameters are not too accurate because we use a small subsets of observations, the change point estimate remains good.
-A two stage change point estimation approach is also possible as explained in \citet{iacyos09}.
+Notice that, even if the estimated parameters are not too accurate because we use a small subsets of observations, the change-point estimate remains good.
+A two stage change-point estimation approach is also possible as explained in \citet{iacyos09}.
-\subsection{LASSO model selection}
+\subsection{LASSO Model Selection}
Let $X_t$ be a diffusion process solution to
$$
\de X_t = b(\alpha, X_t) \de t + \sigma(\beta,X_t) \de W_t
@@ -1154,7 +1148,7 @@
\end{equation}
where $\tilde \alpha_{n,j}$ and $\tilde \beta_{n,k}$ are the unpenalized QML estimator of $\alpha_j$ and $\beta_k$ respectively, $\delta_1, \delta_2>0$ and usually taken unitary.
-\subsection{An example of use}
+\subsection{An Example of Use}
The \code{lasso} method is implemented in the \pkg{yuima} package.
Let us consider the full CKLS model
$$\de X_t = (\alpha+\beta X_t)\de t + \sigma X_t^\gamma\de W_t$$
@@ -1208,65 +1202,3 @@
\end{document}
-
-The YUIMA Project\footnote{The Project has been funded up to 2010 by the Japan Science Technology (JST) Basic Research Programs PRESTO, Grants-in-Aid for Scientific Research No. 19340021.} is an open source\footnote{All code in the \pkg{yuima} package is subject to the GNU General Public License, Version 2, see \url{http://www.gnu.org/licenses/gpl-2.0.html}.}
- academic project aimed at developing the \proglang{R} package named ``\pkg{yuima}'' for simulation and inference of stochastic differential equations.
-The YUIMA Project is mainly developed by mathematicians and
-statisticians who actively publish in the field of inference and simulation for stochastic
-differential equations.
-%The YUIMA Project Core Team, currently
-%consists of the following people: A. Brouste, M. Fukasawa, H. Hino, S.M. Iacus, K. Kamatani, H.Masuda, Y. Shimizu, M. Uchida, N. Yoshida.
-
-
-
- The \pkg{yuima} package provides
-an object-oriented programming environment
-for simulation and statistical inference
-for stochastic processes by \proglang{R}.
-The \pkg{yuima} package adopts the $\tt S4$ system of classes and methods \citep{chambers98}.
-
-Under this framework,
-the \pkg{yuima} package also supplies various functions
-to execute simulation and statistical analysis.
-Both categories of procedures may depend each other.
-Statistical inference often requires a simulation technique
-as a subroutine, and a certain simulation method
-needs to fix a tuning parameter by applying
-a statistical methodology.
-It is especially the case of stochastic processes
-because most of expected values involved
-do not admit an explicit expression.
-The \pkg{yuima} package facilitates comprehensive, systematic approaches
-to the solution.
-
-
-Stochastic differential equations are
-commonly used
-to model random evolution along continuous or
-practically continuous time, such as
-the random movements of a stock price.
-Theory of statistical inference for
-stochastic differential equations already has a fairly long history,
-more than three decades, but it is still developing quickly new
-methodologies and expanding the area.
-The formulas produced by the theory are usually very sophisticated,
-which makes it difficult for practitioners not necessarily
-familiar with this field to enjoy their utility.
-For example, the asymptotic expansion method for computing
-asian option prices (i.e., expectation of a functional of
-a stochastic process) provides precise approximation values
-instantaneously, taking advantage of the analytic approach,
-but the formula, based on Malliavin calculus, has a long expression like more than one page!
-
-
-The \pkg{yuima} package delivers up-to-date methods as a package
-onto the desk of the user working
-with simulation and/or statistics for stochastic differential equations.
-
-
-Sampled data from a continuous-time process features
-the time stamps as well as the positions of the object.
-It is requiring a new theory of estimation.
-The \pkg{yuima} framework can apply multi-dimensional time stamps
-of tick data and provides diverse functions handling such kind data
-to support statistical analysis.
Modified: pkg/yuimadocs/inst/doc/JSS/bibliography.bib
===================================================================
--- pkg/yuimadocs/inst/doc/JSS/bibliography.bib 2011-10-18 07:45:17 UTC (rev 194)
+++ pkg/yuimadocs/inst/doc/JSS/bibliography.bib 2011-11-11 19:48:23 UTC (rev 195)
@@ -13,19 +13,28 @@
@article{iacyos09,
- title = {Estimation for the change point of the volatility in a stochastic differential equation},
+ title = {Estimation for the Change Point of the Volatility in a Stochastic Differential Equation},
author = {Iacus, S.M. and Yoshida, N.},
journal = {http://arxiv.org/abs/0906.3108},
year = {2009}
}
+ at article{zoo,
+title = {zoo: S3 Infrastructure for Regular and Irregular Time Series},
+author = {Achim Zeileis and Gabor Grothendieck},
+journal = {Journal of Statistical Software},
+year = {2005},
+volume = {14},
+number = {6},
+pages = {1--27},
+url = {http://www.jstatsoft.org/v14/i06/},
+}
-
@article{WoodChan,
author={Wood, A. and Chan, G.},
-title={Simulation of stationary Gaussian processes},
+title={Simulation of Stationary Gaussian Processes},
journal={Journal
-of computational and graphical statistics},
+of Computational and Graphical Statistics},
volume={3},
number=4,
year={1994},
@@ -35,8 +44,8 @@
@article{Zou06,
author={Zou, H.},
- title={The adaptive LASSO and its Oracle properties},
- journal={J. Amer. Stat. Assoc.},
+ title={The Adaptive LASSO and its Oracle Properties},
+ journal={Journal of the American Statistical Association},
volume={101},
number=476,
year={2006},
@@ -46,7 +55,7 @@
@article{DegIac10b,
author={De Gregorio, A. and Iacus, S. M.},
- title={Adaptive LASSO-type estimation for ergodic diffusion processes},
+ title={Adaptive LASSO-Type Estimation for Ergodic Diffusion Processes},
journal={Econometric Theory},
year= {forthcoming}
}
@@ -56,8 +65,8 @@
@article{Kessler97,
author={Kessler, M.},
-title={Estimation of an ergodic diffusion from discrete observations},
-journal={Scand. J. Stat.},
+title={Estimation of an Ergodic Diffusion from Discrete Observations},
+journal={Scandinavian Journal of Statistics},
volume={24},
year=1997,
pages={221--229}
@@ -67,7 +76,7 @@
@article{hay-yos05,
author={Hayashi, T. and Yoshida, N.},
- title={On Covariance Estimation of Non-synchronously
+ title={On Covariance Estimation of Non-Synchronously
Observed Diffusion Processes},
journal={Bernoulli},
volume={11},
@@ -78,7 +87,7 @@
@article{hay-yos04,
author={Hayashi, T. and Yoshida, N.},
- title={Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes},
+ title={Asymptotic Normality of a Covariance Estimator for Nonsynchronously Observed Diffusion Processes},
journal={Annals of the Institute of Statistical Mathematics},
volume={60},
issue={2},
@@ -89,7 +98,7 @@
@article{hay-yos06,
author={Hayashi, T. and Yoshida, N.},
title={Nonsynchronous Covariance Estimator and Limit Theorem},
- journal={ Institute of Statistical Mathematics},
+ journal={Institute of Statistical Mathematics},
volume={Research Memorandum No.1020},
year=2006,
pages={1--40}
@@ -105,11 +114,21 @@
pages={1--40}
}
+ at manual{ERRE,
+title = {R: A Language and Environment for Statistical Computing},
+author = {{R Development Core Team}},
+organization = {R Foundation for Statistical Computing},
+address = {Vienna, Austria},
+year = {2011},
+note = {{ISBN} 3-900051-07-0},
+url = {http://www.R-project.org/},
+}
+
@article{Yos05a,
author={Yoshida, N.},
- title={General M-estimation for stochastic differential
- equation with jumps by sampled data},
+ title={General M-estimation for Stochastic Differential
+ Equation with Jumps by Sampled Data},
journal={in preparation},
volume={xxx},
year=2005,
@@ -119,8 +138,8 @@
@article{Yoshida92,
author={Yoshida, N.},
- title={Estimation for diffusion processes from discrete observation},
- journal={J. Multivar. Anal.},
+ title={Estimation for Diffusion Processes from Discrete Observation},
+ journal={Journal of Multivariate Analysis},
volume= {41},
number=2,
year= 1992,
@@ -130,8 +149,8 @@
@article{Yoshida92b,
author={Yoshida, N.},
-title={Asymptotic expansion for statistics related to small diffusions},
-journal={J. Japan Statist. Soc.},
+title={Asymptotic Expansion for Statistics Related to Small Diffusions},
+journal={Journal of the Japan Statistical Society},
volume= {22},
year= 1992,
pages={139--159}
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