[Yuima-commits] r191 - pkg/yuimadocs/inst/doc/JSS

[noreply at r-forge.r-project.org]

Author: iacus
Date: 2011-09-29 04:52:52 +0200 (Thu, 29 Sep 2011)
New Revision: 191

Modified:
   pkg/yuimadocs/inst/doc/JSS/article.Rnw
Log:
update

Modified: pkg/yuimadocs/inst/doc/JSS/article.Rnw
===================================================================
--- pkg/yuimadocs/inst/doc/JSS/article.Rnw	2011-09-27 15:32:58 UTC (rev 190)
+++ pkg/yuimadocs/inst/doc/JSS/article.Rnw	2011-09-29 02:52:52 UTC (rev 191)
@@ -679,9 +679,30 @@
 @
 %The argument \code{method="nomcmc"} in \code{adaBayes} performs numerical
 %integration, otherwise MCMC method is used.
+\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 $T=n^(1/3)$, 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
+<<>>=
+n <- 500
+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 = 0.2, theta2 = 0.3))
+param.init <- list(theta2=0.5,theta1=0.5)
+mle2 <- qmle(yuima, start =param.init , 
+lower = list(theta1=0, theta2=0), 
+upper = list(theta1=1, theta2=1))
+bayes2 <- adaBayes(yuima, start=param.init, prior=prior)
+@
+and we look at the estimates
+<<>>=
+coef(bayes2)
+coef(mle2)
+@
+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}
 Suppose that two It\^o processes are observed
 only at discrete times in a nonsynchronous manner.