Central Limit Theorems for High Dimensional Dependent Data

04/27/2021
by   Jinyuan Chang, et al.
0

Motivated by statistical inference problems in high-dimensional time series analysis, we derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles, simple convex sets and sparsely convex sets. We investigate the quantitative effect of temporal dependence on the rates of convergence to normality over three different dependency frameworks (α-mixing, m-dependent, and physical dependence measure). In particular, we establish new error bounds under the α-mixing framework and derive faster rate over existing results under the physical dependence measure. To implement the proposed results in practical statistical inference problems, we also derive a data-driven parametric bootstrap procedure based on a kernel-type estimator for the long-run covariance matrices.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/12/2020

Statistical Inference for High Dimensional Panel Functional Time Series

In this paper we develop statistical inference tools for high dimensiona...
02/20/2019

Sample Splitting and Weak Assumption Inference For Time Series

We consider the problem of inference after model selection under weak as...
03/19/2021

Gaussian approximation and spatially dependent wild bootstrap for high-dimensional spatial data

In this paper, we establish a high-dimensional CLT for the sample mean o...
09/13/2020

Central Limit Theorem and Bootstrap Approximation in High Dimensions with Near 1/√(n) Rates

Non-asymptotic bounds for Gaussian and bootstrap approximation have rece...
09/24/2018

Moment bounds for autocovariance matrices under dependence

The goal of this paper is to obtain expectation bounds for the deviation...
01/04/2019

Approximating high-dimensional infinite-order U-statistics: statistical and computational guarantees

We study the problem of distributional approximations to high-dimensiona...
03/07/2022

Sequential Gaussian approximation for nonstationary time series in high dimensions

Gaussian couplings of partial sum processes are derived for the high-dim...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.