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.

中文翻译：

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未知非齐方差下基于非参数最大似然估计的高维分类

我们提出了一种基于未知和不等方差下高维均值向量估计的高维分类新方法。我们提出的方法基于一个半参数模型，该模型分别结合了均值和方差的非参数模型和参数模型。我们提出的方法旨在对均值向量的结构具有鲁棒性，而大多数现有方法都是针对某些特定情况开发的，例如均值向量的稀疏或非稀疏情况。此外，我们还考虑在非参数经验贝叶斯框架下分别估计均值和方差，该框架优于现有的基于标准化的非参数经验贝叶斯分类器。我们提出的模拟研究表明，我们提出的方法优于各种现有方法。