TWO NEW ESTIMATORS OF DISTRIBUTION FUNCTIONS

A. K. Md. Ehsanes Saleh, Patrick J. Farrell

Abstract


This paper considers the estimation of a distribution function FX(x) based on
a random sample X1,X2, . . . ,Xn when the sample is suspected to come from a
close-by distribution F0(x). Two new estimators, namely FPT
n (x) and FS
n (x) are
defined and compared with the “empirical distribution function”, Fn(x), under
local departure; that is FX(x) = F0(x) + n−1/2, where maxx|FX(x) − F0(x)|
n−1/2. In this case, we show that FS
n (x) is superior to FPT
n (x) in the neighbour-
hood of F0(x).


Keywords


Empirical Distribution Function; Local Alternatives; Mean Square Error; Preliminary Test Estimator; Shrinkage Estimator.

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ISSN: 0256422X