Simultaneous Inference for High Dimensional Mean Vectors

2017/04/16 by Zhipeng Lou, Lou, Zhipeng, Wei Biao Wu +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1704.04806

openalex publication_date 2017/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X₁, …, X_n∈ℝ^p be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector 𝔼 (X_i) with finite polynomial moments and an ultra high dimension. Our approach is based on the truncated sample mean vector. A Gaussian approximation result is derived for the latter under the very mild finite polynomial ((2+θ)-th) moment condition and the dimension p can be allowed to grow exponentially with the sample size n. Based on this result, we propose an innovative resampling method to construct simultaneous confidence intervals for mean vectors.

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• Two-directional simultaneous inference for high-dimensional models

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