Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 96--105

A COMPARISON OF BIASED AND BIAS-CORRECTED ESTIMATORS

By

THOMAS A. SEVERINI, Northwestern University

SUMMARY. Let $\hat{\theta}$ denote an estimator of a scalar parameter ${\theta}$ based on a sample of size n. Suppose that the expected value of $\hat{\theta}$ maybe written q +a(q )n-1+O(n-2) , where a is a known function. In this case a bias-corrected estimator may be constructed, given by $\tilde{\theta}={\hat{\theta}}-a(\hat{\theta})n^{-1}$. In this paper $\hat{\theta}$ and $tilde{\theta}$ are compared by considering the large-sample properties P{$|\tilde{\theta}-\theta|<|\hat{\theta}-\theta|$}. It is shown that if the bias of $\hat{\theta}$ and the skewness of $\hat{\theta}$ are of opposite signs then $\tilde{\theta}$ is preferable to $\hat{\theta}$; if the bias and skewness of $\hat{\theta}$ have the same sign then $\tilde{\theta}$ is preferable only if the bias is large relative to the skewness.

AMS (1980) subject classification. 62F10, 62F12.

Key words and phrases. Asymptotic theory, maximum likelihood estimation, Pitman nearness, unbiased estimation.

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This article in mathematical reviews.