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Activity Number: 669 - Recent Advances in Nonparametric Statistics
Type: Contributed
Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #322632
Title: An Optimal Semiparametric Method for Two-Group Classification
Author(s): Seungchul Baek* and Osamu Komori and Yanyuan Ma
Companies: University of South Carolina and University of Fukui and Penn State University
Keywords: classification ; discriminant analysis ; semiparametrics ; t-statistic

In the classical discriminant analysis, when two multivariate normal distributions with equal variance-covariance matrices are assumed for two groups, the classical linear discriminant function is optimal with respect to maximizing the standardized difference between the means of two groups. However, for a typical case-control study, the distributional assumption for the case group often needs to be relaxed in practice. Komori et al. (2015) proposed the generalized t-statistic to obtain a linear discriminant function which allows for heterogeneity of case group. Their procedure has an optimality property in the class of consideration. We perform a further study of the problem and show that additional improvement is achievable. The approach we propose does not require a parametric distributional assumption on the case group. We further show that the new estimator is efficient, in that no further improvement is possible to construct the linear discriminant function more efficiently. We conduct simulation studies and a real data example to illustrate the finite sample performance and the gain that it produces in comparison with existing methods.

Authors who are presenting talks have a * after their name.

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