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ESTIMATION OF A DISTRIBUTION FUNCTION DOMINATING STOCHASTICALLY A KNOWN DISTRIBUTION FUNCTION
Author(s) -
Puri Prem S.,
Singh Harshinder
Publication year - 1992
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1992.tb01040.x
Subject(s) - estimator , empirical distribution function , mathematics , cumulative distribution function , statistics , mean squared error , asymptotic distribution , distribution (mathematics) , function (biology) , probability density function , mathematical analysis , evolutionary biology , biology
Summary This paper considers the problem of estimating a cumulative distribution function (cdf), when it is known a priori to dominate a known cdf. The estimator considered is obtained by adjusting the empirical cdf using the prior information. This adjusted estimator is shown to be consistent, its limiting distribution is found, and its mean squared error (MSE) is shown to be smaller than the MSE of the empirical cdf. Its asymptotic efficiency (compared to the empirical cdf) is also found.