Results on double sample estimation for the binomial distribution
type: Item
instance of: scholarly article
title: Results on double sample estimation for the binomial distribution
zbMATH Open document ID: 0545.62050
author: Arthur Cohen
author: Harold B. Sackrowitz
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: The authors consider a sequence of i.i.d. Bernoulli variables with parameter p, 0\(\leq p\leq 1\). A complete class result is obtained for double sample estimation and sequential estimation. The complete class result can be applied to prove that if the loss is a linear combination of squared error and cost of sampling then any estimation procedure (with its sampling rule) where the sample proportion is the terminal decision is inadmissible except for the case where the total sample is a single observation. If the terminal decision loss function is squared error divided by p(1-p) and the overall loss is a linear combination, then any double sample procedure in which the estimate is the sample proportion is inadmissible. These last two results demonstrate the inadmissibility of the Miller- Freund procedure for various linear combination loss functions. Finally, it is shown that the sample proportion as a true double sample estimate is not unbiased.
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62C05
Mathematics Subject Classification ID: 62C15
zbMATH DE Number: 3868450
zbMATH Keywords: vector loss function
zbMATH Keywords: unbiasedness
zbMATH Keywords: binomial distribution
zbMATH Keywords: sequence of i.i.d. Bernoulli variables
zbMATH Keywords: double sample estimation
zbMATH Keywords: inadmissibility of the Miller-Freund procedure
zbMATH Keywords: linear combination loss functions
reviewed by: Volker Mammitzsch
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346728
OpenAlex ID: W2061578342
DOI: 10.1214/AOS/1176346728
description: scientific article; zbMATH DE number 3868450