Electronic Journal of Statistics

High dimensional efficiency with applications to change point tests

John A.D. Aston and Claudia Kirch

Full-text: Open access

Abstract

This paper rigourously introduces the asymptotic concept of high dimensional efficiency which quantifies the detection power of different statistics in high dimensional multivariate settings. It allows for comparisons of different high dimensional methods with different null asymptotics and even different asymptotic behavior such as extremal-type asymptotics. The concept will be used to understand the power behavior of different test statistics as the performance will greatly depend on the assumptions made, such as sparseness or denseness of the signal. The effect of misspecification of the covariance on the power of the tests is also investigated, because in many high dimensional situations estimation of the full dependency (covariance) between the multivariate observations in the panel is often either computationally or even theoretically infeasible. The theoretic quantification by the theory is accompanied by simulation results which confirm the theoretic (asymptotic) findings for surprisingly small samples. The development of this concept was motivated by, but is by no means limited to, high-dimensional change point tests. It is shown that the concept of high dimensional efficiency is indeed suitable to describe small sample power.

Article information

Source
Electron. J. Statist., Volume 12, Number 1 (2018), 1901-1947.

Dates
Received: November 2017
First available in Project Euclid: 14 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1528941678

Digital Object Identifier
doi:10.1214/18-EJS1442

Mathematical Reviews number (MathSciNet)
MR3815301

Zentralblatt MATH identifier
06890102

Subjects
Primary: 62F05: Asymptotic properties of tests 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G10: Hypothesis testing

Keywords
CUSUM high dimensional efficiency model misspecification panel data projections

Rights
Creative Commons Attribution 4.0 International License.

Citation

Aston, John A.D.; Kirch, Claudia. High dimensional efficiency with applications to change point tests. Electron. J. Statist. 12 (2018), no. 1, 1901--1947. doi:10.1214/18-EJS1442. https://projecteuclid.org/euclid.ejs/1528941678


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