Statistica Sinica 14(2004), 1021-1036

USING KULLBACK-LEIBLER INFORMATION FOR MODEL

SELECTION WHEN THE DATA-GENERATING MODEL IS

UNKNOWN: APPLICATIONS TO GENETIC

TESTING PROBLEMS

Gang Zheng$^{1}$, Boris Freidlin$^2$ and Joseph L. Gastwirth$^{2,3}$

$^1$National Heart, Lung and Blood Institute, $^2$National Cancer Institute

and $^3$George Washington University

Abstract: In genetic studies of complex diseases the underlying genetic model is usually unknown. Thus, a family of locally optimal statistics is obtained for testing association or linkage. Utilizing two new measures based on Kullback-Leibler information, we are able to define a family of admissible genetic models and obtain the corresponding two optimality criteria to select robust models. The model selection procedures described in this paper are valid regardless of sample size. The results are applied to genetic linkage analysis using affected sibs and candidate-gene association tests using the case-parents design. Our results provide insight into some commonly used statistics in the genetic linkage analysis of affected sib-pairs.

Key words and phrases: Admissible genetic model, association and linkage, Kullback-Leibler information, maximin, minimax, robustness.