High‐dimensional classification based on nonparametric maximum likelihood estimation under unknown and inhomogeneous variances

We propose a new method in high‐dimensional classification based on estimation of high‐dimensional mean vector under unknown and unequal variances. Our proposed method is based on a semi‐parametric model that combines nonparametric and parametric models for mean and variance, respectively. Our proposed method is designed to be robust to the structure of the mean vector, while most existing methods are developed for some specific cases such as either sparse or non‐sparse case of the mean vector. In addition, we also consider estimating mean and variance separately under nonparametric empirical Bayes framework that has advantage over existing nonparametric empirical Bayes classifiers based on standardization. We present simulation studies showing that our proposed method outperforms a variety of existing methods. Application to real data sets demonstrates robustness of our method to various types of data sets, while all other methods produce either sensitive or poor results for different data sets.