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Martin Sleziak
Martin Sleziak
5:25 AM
Another new tag delta-method was created by glowstonetrees. The tag-info is currently empty.
1
Q: Using the delta method to find the asymptotic distribution

glowstonetreesThe Question: Given independent random variables $X_1, \dots,X_n \sim N(\mu,\mu^2)$, let $Q=\sum_{i=1}^n(X_i-\overline X)^2$ where $\overline X = \frac 1n \sum_{i=1}^nX_i$. Use the delta method to find the asymptotic distribution of $\frac 13\Bigl(\overline X+2\sqrt{\frac{Q}{n-1}}\Bigr)$. My...

statistics asymptotics normal-distribution delta-method
0
Q: Asymptotic variance of the median

glowstonetreesThe Question: You are given that if $U_1,\dots,U_n \sim \text{ Uniform}[0,1]$ are iid, and $M_U$ is the sample median, then $$\Bbb E[M_U]=\frac 12 \qquad \qquad \text{Var}\,(M_U) = \frac{1}{4(n+2)}$$ Let $X_i=F^{-1}(U_i)$ for $i=1,\dots,n$, so that $X_1,\dots,X_n$ are iid with from a distribut...

statistics asymptotics median delta-method
Delta method
In statistics, the delta method is a result concerning the approximate probability distribution for a function of an asymptotically normal statistical estimator from knowledge of the limiting variance of that estimator. It was first described in 1938 by Robert Dorfman == Univariate delta method == While the delta method generalizes easily to a multivariate setting, careful motivation of the technique is more easily demonstrated in univariate terms. Roughly, if there is a sequence of random variables Xn satisfying n ...
 
 
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Martin Sleziak
Martin Sleziak
10:48 AM
 

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