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THE COVARIANCE ADJUSTED LOCATION LINEAR

DISCRIMINANT FUNCTION FOR CLASSIFYING DATA WITH

UNEQUAL DISPERSION MATRICES IN DIFFERENT LOCATIONS

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CHI-YING LEUNG

*Department of Statistics, The Chinese University of Hong Kong,*

Shatin, New Territories, Hong Kong, China
(Received June 26, 1995; revised May 21, 1997)

**Abstract.**
Classification between two
populations dealing with both continuous and binary
variables is handled by splitting the problem into
different locations. Given the location specified by the
values of the binary variables, discrimination is
performed using the continuous variables. The location
probability model with homoscedastic across location
conditional dispersion matrices is adopted for this
problem. In this paper, we consider presence of continuous
covariates with heterogeneous location conditional
dispersion matrices. The continuous covariates have equal
location specific mean in both populations. Conditional
homoscedasticity fails when strong interaction between the
continuous and binary variables is present. A plug-in
covariance adjusted rule is constructed and its asymptotic
distribution is derived. An asymptotic expansion for the
overall error rate is given. The result is extended to
include binary covariates.

*Key words and phrases*:
Location linear
discriminant function, covariance adjustment,
heteroscedastic conditional dispersion matrices, overall
expected error rate.

**Source**
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