Coordinatewise Gaussianization: Theories and Applications

Qing Mai, Di He and Hui Zou

Journal of the American Statistical Association, 2023, vol. 118, issue 544, 2329-2343

Abstract: In statistical analysis, researchers often perform coordinatewise Gaussianization such that each variable is marginally normal. The normal score transformation is a method for coordinatewise Gaussianization and is widely used in statistics, econometrics, genetics and other areas. However, few studies exist on the theoretical properties of the normal score transformation, especially in high-dimensional problems where the dimension p diverges with the sample size n. In this article, we show that the normal score transformation uniformly converges to its population counterpart even when log p=o(n/ log n). Our result can justify the normal score transformation prior to any downstream statistical method to which the theoretical normal transformation is beneficial. The same results are established for the Winsorized normal transformation, another popular choice for coordinatewise Gaussianization. We demonstrate the benefits of coordinatewise Gaussianization by studying its applications to the Gaussian copula model, the nearest shrunken centroids classifier and distance correlation. The benefits are clearly shown in theory and supported by numerical studies. Moreover, we also point out scenarios where coordinatewise Gaussinization does not help and even causes damages. We offer a general recommendation on how to use coordinatewise Gaussianization in applications. Supplementary materials for this article are available online.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2022.2044825 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:118:y:2023:i:544:p:2329-2343

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2022.2044825

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().