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

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.

authors

• Zhou, Quan

published proceedings

• STATISTICS & PROBABILITY LETTERS

author list (cited authors)

• Peng, S., & Zhou, Q.

citation count

• 8

complete list of authors

• Peng, Shige||Zhou, Quan

publication date

• January 2020

publisher

• Elsevier  Publisher

published in

• Statistics and Probability Letters  Journal

keywords

• Heteroskedasticity
• Nonlinear Heat Equation
• P-hacking
• Sublinear Expectation
• Tail Capacity

Digital Object Identifier (DOI)

• 10.1016/j.spl.2019.108623

start page

• 108623

end page

• 108623

volume

• 156

URL

• http://dx.doi.org/10.1016/j.spl.2019.108623