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Statistica Sinica 4(1994), 169-185


ESTIMATION IN THE EXPONENTIAL FAMILY IN

THE PRESENCE OF NUISANCE PARAMETERS:

COMPROMISE BETWEEN BIAS AND PRECISION


Yue-Cune Chang and Kung-Yee Liang


Academia Sinica and Johns Hopkins University


Abstract: The estimation of the common odds ratio in one-to-one matched case-control studies is a typical example of the trade-off between bias and precision in public health research. Liang and Zeger (1988) proposed an estimator through estimating functions. An alternative approach motivated by reducing asymptotic MSE was presented by Kalish (1990). In this paper, a finite sample approach is conducted under a more general framework. Comparisons for pair-matched case-control studies are made among these three estimators in terms of bias, MSE, coverage probability, and length of confidence interval. Extension to the multidimensional case is also presented.



Key words and phrases: Bias, case-control study, conditional likelihood, empirical bayes, estimating functions, profile likelihood, simulation.



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