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In this study, we introduce an innovative methodology aimed at enhancingFisher's Linear Discriminant Analysis (LDA) in the context of high-dimensionaldata classification scenarios, specifically addressing situations where eachfeature exhibits distinct variances. Our approach leverages NonparametricMaximum Likelihood Estimation (NPMLE) techniques to estimate both the mean andvariance parameters. By accommodating varying variances among features, ourproposed method leads to notable improvements in classification performance. Inparticular, unlike numerous prior studies that assume the distribution ofheterogeneous variances follows a right-skewed inverse gamma distribution, ourproposed method demonstrates excellent performance even when the distributionof heterogeneous variances takes on left-skewed, symmetric, or right-skewedforms. We conducted a series of rigorous experiments to empirically validatethe effectiveness of our approach. The results of these experiments demonstratethat our proposed methodology excels in accurately classifying high-dimensionaldata characterized by heterogeneous variances.

Nonparametric Mean and Variance Adaptive Classification Rule for High-Dimensional Data with Heteroscedastic Variances