Bias-variance tradeoff : Forabinomialparameter , considertheBayesianestimator (Y + 1)~(n + 2) that occurswithauniformpriordistribution. (a) Deriveitsbiasanditsvariance.ComparethesewiththebiasandvarianceoftheML estimator
Question:
Bias-variance tradeoff : Forabinomialparameter π, considertheBayesianestimator (Y +
1)~(n + 2) that occurswithauniformpriordistribution.
(a) Deriveitsbiasanditsvariance.ComparethesewiththebiasandvarianceoftheML estimator ˆπ = Y ~n.
(b) ShowthatitsMSE = [nπ(1−π)+(1−2π)2]~(n+2)2. For n = 10 and for n = 1000, plotthis and theMSEoftheMLestimatorasafunctionof π. Describethe π valuesforwhichthe MSE issmallerfortheBayesestimator.Explainhowthisreflectsitsshrinkagetoward 1/2 andthebias/variancetradeoff.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Foundations Of Statistics For Data Scientists With R And Python
ISBN: 9780367748456
1st Edition
Authors: Alan Agresti
Question Posted: