Substituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, use this theorem to rework Exercise 10.35.
Answer to relevant QuestionsTo show that an estimator can be consistent with-out being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ2, we first ...If X1 and X2 constitute a random sample of size n = 2 from a Poisson population, show that the mean of the sample is a sufficient estimator of the parameter λ. Given a random sample of size n from a continuous uniform population, use the method of moments to find formulas for estimating the parameters α and β. Given a random sample of size n from a Rayleigh population (see Exercise 6.20 on page 184), find an estimator for its parameter α by the method of maximum likelihood. Let X1, X2, . . . , Xn be a random sample of size n from the uniform population given by Show that if Y1 and Yn are the first and nth order statistic, any estimator Θ such that Can serve as a maximum likelihood estimator of ...
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