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Title: | Estimating the parameter of the population selected from discrete exponential family |
Authors: | VELLAISAMY, P JAIN, S |
Keywords: | Quantile Estimation Poisson |
Issue Date: | 2008 |
Publisher: | ELSEVIER SCIENCE BV |
Citation: | STATISTICS & PROBABILITY LETTERS, 78(9), 1076-1087 |
Abstract: | Let X-1, ..., X-p be p independent random observations, where X-i is from the ith discrete population with density of the form u(i)(theta(i))t(i)(x(i))theta(xi)(i), where theta(i) is the positive unknown parameter. Let X-(1) = ... = X-(l) > X(l+1) >= ... >= X-(m) > X(m+1) = ... = X-(p) denote the ordered observations, where the ordering is done from the largest to the smallest and from smaller index to larger ones, among equal observations. Suppose the population corresponding to X-(1) (or X(m+1)) is selected, and theta((i)) denotes the parameter associated with X-(i), 1 <= i <= p. In this paper, we consider the estimation of theta((1)) (or theta((m+1))) under the loss L-k (t, theta) = (t - theta)(2)/theta(k), for k >= 0, an integer. We construct explicit estimators, specifically for the cases k = 0 and k = 1, of theta((1)) and theta((m+1)) that dominate the natural estimators, by solving certain difference inequalities. In particular, improved estimators for the selected Poisson and negative binomial distributions are also presented. (c) 2007 |
URI: | http://dx.doi.org/10.1016/j.spl.2007.11.001 http://dspace.library.iitb.ac.in/xmlui/handle/10054/6582 http://hdl.handle.net/10054/6582 |
ISSN: | 0167-7152 |
Appears in Collections: | Article |
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