Interval estimation in two-group discriminant analysis under heteroscedasticity for large dimension

Takayuki Yamada

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 23, 5717-5728

Abstract: This article is concerned with the problem of discriminating between two populations with heteroscedastic multivariate normal distributions based on an observation vector x$\mbox{$\boldsymbol{x}$}$. We give the limiting distribution of the unbiased estimator for the log odds ratio of the posterior probabilities as the sample sizes Ni (i = 1, 2) and the dimension p go to infinity together with the ratio p/(Ni − 1) converging a finite non zero constant ci ∈ (0, 1) for the case in which the prior probabilities are equal. Approximated interval estimation for the log odds ratio is derived. Simulation results indicate that our estimation has good accuracy compared with the classical results.

Date: 2018
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DOI: 10.1080/03610926.2017.1400060

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