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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), 10761087 
Abstract:  Let X1, ..., Xp be p independent random observations, where Xi 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 Lk (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:  01677152 
Appears in Collections:  Article

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