parametric bootstrap.htm

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<H2><A name=SECTION00313000000000000000>Parametric bootstrap</A> </H2>If one has 
a parametric distribution <IMG height=17 alt=$F_\lambda$ 
src="Parametric bootstrap.files/img305.png" width=16 align=middle border=0> 
which is well defined except for the pamameter <IMG height=34 alt=$\lambda$ 
src="Parametric bootstrap.files/img306.png" width=26 align=bottom border=0>, 
instead of drawing with replacement from the original sample, one can draw from 
the distribution <!-- MATH $F_{\widehat{\lambda}}$ --><IMG height=23 
alt=$F_{\widehat{\lambda}}$ src="Parametric bootstrap.files/img307.png" width=16 
align=middle border=0>, where <!-- MATH $\widehat{\lambda}$ --><IMG height=34 
alt=$\widehat{\lambda}$ src="Parametric bootstrap.files/img308.png" width=26 
align=bottom border=0> is the estimation obtained from the original sample. 
<P><PRE>#Parametric Bootstrap
"boot.par"&lt;-
function(model.sim = law.sim, n = 15, nboot = 66)
{
#Parametric bootstrap of correlation coefficient
#Law sim contains bivariate normal data

        theta &lt;- rep(0, nboot)
        for(b in (1:nboot))
                theta[b] &lt;- corr(((b - 1) * n + 1):(b * n), law.sim)
        return(theta)
}


#Example of using the functions and plotting the results

n1 &lt;- rnorm(1000)
n2 &lt;- rnorm(1000)
law.sim &lt;- cbind(n1, 0.777 * n1 + sqrt(1 - (0.777^2)) * n2)
rbootpar &lt;- boot.par()
hist(rbootpar)
par(new=T)
plot(density(rbootpar, width = 0.15), xlab = "", ylab = "",
 lab = c(0, 0, 0),type = "l")
title("Parametric Bootstrap - Law School corr.", cex = 1.9)
</PRE>
<P><BR>
<HR>

<ADDRESS>Susan Holmes 2002-01-12 </ADDRESS></BODY></HTML>

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