Year: 2017
Type: preprint
Abstract: Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ 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.
Source: arXiv (Cornell University)
Authors: Lou, Zhipeng, Wu, Wei Biao
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2605670822