(b) Assume that n independent count variables {X,X,...,X,} are identically distributed as X, ~ Poi(0) where i=1,2,...,n and to estimate E(X;)=0 , consider the sample mean estimator ê = -X,. (i) Describe the distribution of the random variable S=nô. Use the expectation of the distribution of S = nỗ to compute the expectation E(Ô) and the bias of this estimator. State whether this estimator unbiased. (ii) (iii) Use the variance of the distribution of S=nô to examine var(@) and the standard error of this estimator. Use the variance and the bias of ê to compute the Mean Squaled Eifor (MSE) of this estimator. Comment on the MSE behaviour in the asymptotic limit as n → n. State whether this estimator is consistent or not (iv)
(b) Assume that n independent count variables {X,X,...,X,} are identically distributed as X, ~ Poi(0) where i=1,2,...,n and to estimate E(X;)=0 , consider the sample mean estimator ê = -X,. (i) Describe the distribution of the random variable S=nô. Use the expectation of the distribution of S = nỗ to compute the expectation E(Ô) and the bias of this estimator. State whether this estimator unbiased. (ii) (iii) Use the variance of the distribution of S=nô to examine var(@) and the standard error of this estimator. Use the variance and the bias of ê to compute the Mean Squaled Eifor (MSE) of this estimator. Comment on the MSE behaviour in the asymptotic limit as n → n. State whether this estimator is consistent or not (iv)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:(b)
Assume that n independent count variables {X,,X2,...,X„} are identically
distributed as X, ~ Poi(0) where i=1,2,...,n and to estimate E(X,)=0 , consider
the sample mean estimator ô = - X,.
n iel
(i)
Describe the distribution of the random variable S = nô.
Use the expectation of the distribution of S = nô to compute the expectation
E(Ô) and the bias of this estimator. State whether this estimator unbiased.
(ii)
(ii)
Use the variance of the distribution of S=nn to examine var(@) and the
standard error of this estimator.
Use the variance and the bias of ô to compute the Mean Squaied Eifor
(MSE) of this estimator. Comment on the MSE behaviour in the asymptotic
limit as n→ 0. State whether this estimator is consistent or not
(iv)
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