A hypothesis-testing perspective on the G-normal distribution theory

Shige Peng and Quan Zhou

Statistics & Probability Letters, 2020, vol. 156, issue C

Abstract: The G-normal distribution was introduced by Peng (2007) as the limiting distribution in the central limit theorem for sublinear expectation spaces. Equivalently, it can be interpreted as the solution to a stochastic control problem where we have a sequence of random variables, whose variances can be chosen based on all past information. In this note we study the tail behavior of the G-normal distribution through analyzing a nonlinear heat equation. Asymptotic results are provided so that the tail “probabilities” can be easily evaluated with high accuracy. This study also has a significant impact on the hypothesis testing theory for heteroscedastic data; we show that even if the data are generated under the null hypothesis, it is possible to cheat and attain statistical significance by sequentially manipulating the error variances of the observations.

Keywords: Heteroskedasticity; Nonlinear heat equation; p-hacking; Sublinear expectation; Tail capacity (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016771521930269X
Full text for ScienceDirect subscribers only

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:eee:stapro:v:156:y:2020:i:c:s016771521930269x

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2019.108623

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().