Randomized response surveys of finite populations: A unified approach with quantitative data
type: Item
instance of: scholarly article
title: Randomized response surveys of finite populations: A unified approach with quantitative data
zbMATH Open document ID: 0615.62009
DOI: 10.1016/0378-3758(86)90094-7
author: A. Chaudhry
published in: Journal of Statistical Planning and Inference
publication date: 1987-01-01T00:00:00Z
review text: The obtained results follow suggestions of \textit{M. E. Thompson} [Discussion of the paper by \textit{A. K. Adhikari}, \textit{A. Chaudhuri} and \textit{K. Vijayan}, Int. Stat. Rev. 52, 115-125 (1984; Zbl 0579.62007)]. A random response mechanism generates variables \(Z_ i\) independently and they are related with the true variable value \(Y_ i\) through a model such that \(E_ R(Z_ i)=a_ iY_ i+b_ i\) and \(E_ R(Z^ 2_ i)=a_ iY^ 2_ i+d_ i\). \(a_ i\), \(b_ i\) and \(d_ i\) are known variables and \(E_ R\) is the expectation with respect to the random response technique used. Two models \((M_ 1,M_ 2)\) are proposed for studying the behaviour of strategies. They fix certain properties of expectations, variances and covariances of the \(Y_ i's\). Classes of estimators are constructed. The non-existence of uniformly minimum variance estimators is proved in Theorem 1 for the class \(C_ 1\). Theorem 2 proves the optimality of a certain strategy in the class \(C_ 2\) under \(M_ 2\) and in \(C_ 1\) if \(M_ 1\) is acceptable. When the linear correlation coefficient is zero \((M_ 3)\) the estimator proposed has always better results and if the \textit{V. P. Godambe} and \textit{M. E. Thompson} permutation model \((M_ 4)\) [Ann. Stat. 1, 1212-1221 (1973; Zbl 0275.62011)] holds the strategy still is optimum in \(C_ 1.\) The paper brings an analysis of the optimality of the estimator when direct response is used. Different unequal probability strategies are studied and the errors formulae are worked out.
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 62C05
zbMATH DE Number: 3996836
zbMATH Keywords: randomized response
zbMATH Keywords: finite populations
zbMATH Keywords: optimal strategies
zbMATH Keywords: unequal probability sampling
zbMATH Keywords: non-existence
zbMATH Keywords: uniformly minimum variance estimators
zbMATH Keywords: unequal probability strategies
reviewed by: Carlos Narciso Bouza Herrera
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90094-7
OpenAlex ID: W2004811437
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description: scientific article; zbMATH DE number 3996836