Article ID Journal Published Year Pages File Type
7547671 Statistical Methodology 2016 11 Pages PDF
Abstract
A problem for estimating the number of trials n in the binomial distribution B(n,p), is revisited by considering the large sample model N(μ,cμ) and the associated maximum likelihood estimator (MLE) and some sequential procedures. Asymptotic properties of the MLE of n via the normal model N(μ,cμ) are briefly described. Beyond the asymptotic properties, our main focus is on the sequential estimation of n. Let X1,X2,…,Xm,… be iid N(μ,cμ)(c>0) random variables with an unknown mean μ=1,2,… and variance cμ, where c is known. The sequential estimation of μ is explored by a method initiated by Robbins (1970) and further pursued by Khan (1973). Various properties of the procedure including the error probability and the expected sample size are determined. An asymptotic optimality of the procedure is given. Sequential interval estimation and point estimation are also briefly discussed.
Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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