Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Luis Mendo ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2012, vol. 21, issue 4, 656-675

Abstract: Sequential estimation of the success probability p in inverse binomial sampling is considered in this paper. For any estimator $\hat{p}$ , its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters a and b for $\hat{p}> p$ and $\hat{p}> p$ , respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as p→0, and which guarantee that, for any p∈(0,1), the risk is lower than its asymptotic value. This allows selecting the required number of successes, r, to meet a prescribed quality irrespective of the unknown p. In addition, the proposed estimators are shown to be approximately minimax when a/b does not deviate too much from 1, and asymptotically minimax as r→∞ when a=b. Copyright Sociedad de Estadística e Investigación Operativa 2012

Keywords: Sequential estimation; Point estimator; Inverse binomial sampling; Asymmetric loss function; 62L12; 62F12 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11749-011-0267-x

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