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Fisher Information in Weighted Distributions (1998)
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BibTeX
@MISC{Iyengar98fisherinformation,
author = {Satish Iyengar and Satish Iyengar and Paul Kvam and Harshinder Singh},
title = {Fisher Information in Weighted Distributions},
year = {1998}
}
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Abstract
Standard inference procedures assume a random sample from a population with density f # (x) for estimating the parameter #. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) # 0, and constructed a weighted distribution with a density f w # (x) that is proportional to w(x)f # (x). In this paper, we assume that f # (x) belongs to an exponential family, and study the Fisher information about # in observations obtained from some commonly arising weighted distributions: (i)thek th order statistic of a random sample of size m,(ii) observations from the stationary distribution of the residual lifetime of a renewal process, and (iii) truncated distributions. We give general conditions under which the weighted distribution has greater Fisher information than the original distribution, and specialize to the normal, gamma, and Weibull distributions. These conditions involve the distribution...
Keyphrases
weighted distribution fisher information random sample renewal process residual lifetime original distribution available data many application weibull distribution thek th order statistic general condition exponential family stationary distribution biased sample weight function standard inference procedure
