Comparison of some common ratio estimators using pitman measure of nearness

Lee, Carl M.-S.; Peddada, Shyamal D.

doi:10.1080/03610928708829488

Cited by 7 publications

(1 citation statement)

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“…agreeing that PN is an interesting, intrinsic criterion for comparing estimators, several studies have been conducted using PN to evaluate a variety of different estimators. For example, Rao, Keating, and Mason (1986) develop a general theory to compute PN for univariate estimators, Dyer and Keating (1981) and Keating and Gupta (1984) use PN to compare particular types of scale estimators, Keating (1983) considers estimators of percentiles of location and scale using PN, and Lee and Peddada (1987) compare ratio estimators. Several papers have made comparisons of biased regression estimators using PN, e.g., Keating and Czitrom (1987), Keating and Mason (1988), Conerly and Hardin (1990), and Mason, Keating, Sen, and Blaylock (1990).…”

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confidence: 99%

Shrunken estimators via a pitman nearness criterion

Conerly

Hardin

1991

Communications in Statistics - Theory and Methods

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Shrunken estimators have traditionally been developed and studied using mean square error (MSE). Recent research on Pitman nearness (PN), however, indicates that it is an interesting, "intrinsicIt, alternative to the mean square error (MSE) criterion for investigating estimators. Thus, we develop a shrunken estimator for the mean of a multivariate normal distribution based on minimizing PN, instead of MSE. Further, since the shrinkage factor of this estimator depends on unknown parameters, we examine two approaches for determining this factor: (1) ttplug-inu estimates, (2) a range of values for the factor based on an approximate confidence interval for the Pitman Nearness probability. A numerical example is given.

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