[Yuima-commits] r142 - pkg/yuima/man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Mon Jan 3 04:28:32 CET 2011
Author: hinohide
Date: 2011-01-03 04:28:32 +0100 (Mon, 03 Jan 2011)
New Revision: 142
Added:
pkg/yuima/man/qmle.Rd
Log:
ml.ql and ql are replaced with qmle and quasilogl
Added: pkg/yuima/man/qmle.Rd
===================================================================
--- pkg/yuima/man/qmle.Rd (rev 0)
+++ pkg/yuima/man/qmle.Rd 2011-01-03 03:28:32 UTC (rev 142)
@@ -0,0 +1,198 @@
+\name{qmle}
+%\alias{ql}
+%\alias{ml.ql}
+\alias{qmle}
+\alias{quasilogl}
+%\alias{LSE}
+%\alias{ml.ql2}
+\alias{rql}
+\alias{lse}
+%\alias{ql,ANY-method}
+%\alias{ml.ql,ANY-method}
+%\alias{ml.ql2,ANY-method}
+%\alias{rql,ANY-method}
+\title{Calculate quasi-likelihood and ML estimator of least squares estimator}
+\description{Calculate the quasi-likelihood and estimate of the parameters of the
+ stochastic differential equation by the maximum likelihood method or least squares estimator
+ of the drift parameter.}
+\usage{
+%ml.ql(yuima,theta2,theta1,h,theta2.lim=matrix(c(0,1),1,2),theta1.lim=matrix(c(0,1),1,2),print=FALSE,method,param,interval)
+%ql(yuima,theta2,theta1,h,print=FALSE,param)
+%rql(yuima,theta2,theta1,ptheta2,ptheta1,h,print=FALSE,param,prevparam)
+qmle(yuima, start, method="BFGS", fixed = list(), print=FALSE, lower, upper, joint=FALSE, ...)
+quasilogl(yuima, param, print=FALSE)
+}
+\arguments{
+ \item{yuima}{a yuima object.}
+% \item{theta2,theta1}{parameters of the sdeModel.}
+% \item{h}{ time span of observations.}
+% \item{theta2.lim, theta1.lim}{matrixes to specify the domains of the
+% parameters. Vector can be available only if theta is a scalar.}
+% \item{ptheta2,ptheta1}{}
+ \item{print}{you can see a progress of the estimation when print is TRUE.}
+ \item{method}{see Details.}
+ \item{param}{\code{list} of parameters for the quasi loglikelihood.}
+% \item{interval}{}
+% \item{prevparam}{}
+ \item{lower}{a named list for specifying lower bounds of parameters}
+ \item{upper}{a named list for specifying upper bounds of parameters}
+ \item{start}{initial values to be passed to the optimizer.}
+ \item{fixed}{for conditional (quasi)maximum likelihood estimation.}
+ \item{joint}{perform joint estimation or two stage estimation? by default \code{joint=FALSE}.}
+ \item{...}{passed to \code{\link{optim}} method. See Examples.}
+}
+\details{
+% A function ql calculate the quasi-likelihood of a time series data X with any
+% parameters. A function ml.pl estimates parameters of the sdeModel by
+% maximizing the quasi-likelihood.
+ \code{qmle} behaves more likely the standard \code{mle} function in \pkg{stats4} and
+ argument \code{method} is one of the methods available in \code{\link{optim}}.
+
+ \code{lse} calculates least squares estimators of the drift parameters. This is
+ useful for initial guess of \code{qmle} estimation.
+
+ \code{quasilogl} returns the valueof the quasi loglikelihood for a given
+ \code{yuima} object and list of parameters \code{coef}.
+
+}
+\value{
+ \item{QL}{a real value.}
+ \item{opt}{a list with components the same as 'optim' function.}
+}
+\author{The YUIMA Project Team}
+\note{
+ %The function ml.ql uses the function optim internally.
+ The function qmle uses the function optim internally.
+}
+\examples{
+#dXt^e = -theta2 * Xt^e * dt + theta1 * dWt
+diff.matrix <- matrix(c("theta1"), 1, 1)
+ymodel <- setModel(drift=c("(-1)*theta2*x"), diffusion=diff.matrix, time.variable="t", state.variable="x", solve.variable="x")
+n <- 100
+
+ysamp <- setSampling(Terminal=(n)^(1/3), n=n)
+yuima <- setYuima(model=ymodel, sampling=ysamp)
+set.seed(123)
+yuima <- simulate(yuima, xinit=1, true.parameter=list(theta1=0.3,
+theta2=0.1))
+QL <- quasilogl(yuima, param=list(theta2=0.8, theta1=0.7))
+##QL <- ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)))
+QL
+
+## another way of parameter specification
+##param <- list(theta2=0.8, theta1=0.7)
+##QL <- ql(yuima, h=1/((n)^(2/3)), param=param)
+##QL
+
+
+## old code
+##system.time(
+##opt <- ml.ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)), c(0, 1), c(0, 1))
+##)
+##cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+##print(coef(opt))
+
+
+system.time(
+opt2 <- qmle(yuima, start=list(theta1=0.8, theta2=0.7), lower=list(theta1=0,theta2=0),
+ upper=list(theta1=1,theta2=1), method="L-BFGS-B")
+)
+cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+print(coef(opt2))
+
+## initial guess for theta2 by least squares estimator
+tmp <- lse(yuima, start=list(theta2=0.7), lower=list(theta2=0), upper=list(theta2=1))
+tmp
+
+system.time(
+opt3 <- qmle(yuima, start=list(theta1=0.8, theta2=tmp), lower=list(theta1=0,theta2=0),
+ upper=list(theta1=1,theta2=1), method="L-BFGS-B")
+)
+cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+print(coef(opt3))
+
+
+## perform joint estimation? Non-optimal, just for didactic purposes
+system.time(
+opt4 <- qmle(yuima, start=list(theta1=0.8, theta2=0.7), lower=list(theta1=0,theta2=0),
+ upper=list(theta1=1,theta2=1), method="L-BFGS-B", joint=TRUE)
+)
+cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+print(coef(opt4))
+
+## old code
+##system.time(
+##opt <- ml.ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)), c(0, 1), c(0, 1), method="Newton")
+##)
+##cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+##print(coef(opt))
+
+
+
+
+###multidimension case
+##dXt^e = - drift.matrix * Xt^e * dt + diff.matrix * dWt
+diff.matrix <- matrix(c("theta1.1","theta1.2", "1", "1"), 2, 2)
+
+drift.c <- c("-theta2.1*x1", "-theta2.2*x2", "-theta2.2", "-theta2.1")
+drift.matrix <- matrix(drift.c, 2, 2)
+
+ymodel <- setModel(drift=drift.matrix, diffusion=diff.matrix, time.variable="t",
+ state.variable=c("x1", "x2"), solve.variable=c("x1", "x2"))
+n <- 100
+ysamp <- setSampling(Terminal=(n)^(1/3), n=n)
+yuima <- setYuima(model=ymodel, sampling=ysamp)
+set.seed(123)
+
+##xinit=c(x1, x2) #true.parameter=c(theta2.1, theta2.2, theta1.1, theta1.2)
+yuima <- simulate(yuima, xinit=c(1, 1), true.parameter=list(theta2.1=0.5, theta2.2=0.3, theta1.1=0.6, theta1.2=0.2))
+
+## theta2 <- c(0.8, 0.2) #c(theta2.1, theta2.2)
+##theta1 <- c(0.7, 0.1) #c(theta1.1, theta1.2)
+## QL <- ql(yuima, theta2, theta1, h=1/((n)^(2/3)))
+## QL
+
+## ## another way of parameter specification
+## #param <- list(theta2=theta2, theta1=theta1)
+## #QL <- ql(yuima, h=1/((n)^(2/3)), param=param)
+## #QL
+
+## theta2.1.lim <- c(0, 1)
+## theta2.2.lim <- c(0, 1)
+## theta1.1.lim <- c(0, 1)
+## theta1.2.lim <- c(0, 1)
+## theta2.lim <- t( matrix( c(theta2.1.lim, theta2.2.lim), 2, 2) )
+## theta1.lim <- t( matrix( c(theta1.1.lim, theta1.2.lim), 2, 2) )
+
+## system.time(
+## opt <- ml.ql(yuima, theta2, theta1, h=1/((n)^(2/3)), theta2.lim, theta1.lim)
+## )
+## opt at coef
+
+system.time(
+opt2 <- qmle(yuima, start=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1),
+ lower=list(theta1.1=.1,theta1.2=.1,theta2.1=.1,theta2.2=.1),
+ upper=list(theta1.1=4,theta1.2=4,theta2.1=4,theta2.2=4), method="L-BFGS-B")
+)
+opt2 at coef
+summary(opt2)
+
+## unconstrained optimization
+system.time(
+opt3 <- qmle(yuima, start=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1))
+)
+opt3 at coef
+summary(opt3)
+
+
+quasilogl(yuima, param=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1))
+
+##system.time(
+##opt <- ml.ql(yuima, theta2, theta1, h=1/((n)^(2/3)), theta2.lim, theta1.lim, method="Newton")
+##)
+##opt at coef
+##}
+
+% Add one or more standard keywords, see file 'KEYWORDS' in the
+% R documentation directory.
+\keyword{ts}
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