Statistical test corrections for the skew-t regression model in small samples

Abstract The skew- t model remains an active area of research due to its attractive properties, such as the ability to fit heavy tails and skewness, which allow for a wide range of practical applications, including econometrics and finance. Our goal is to draw conclusions about the population through regression models using the signed ratio test, the likelihood ratio test, and the gradient test. Asymptotic statistical distributions are not recommended when the sample size is small, in which case corrections to the statistical tests should be considered. To date, there have been no such developments in the literature for the skew- t model in this context. In this work, we develop a Fraser-Reid-Wu type correction for the signed ratio test, as well as Bartlett bootstrap and Bartlett-type bootstrap corrections for the likelihood ratio test and the gradient test, respectively. The size and power of the tests and their corrections are analyzed through a simulation study. The original tests exhibit liberal behavior in small samples, whereas the corrected versions are closer to their nominal levels. In terms of power, both the original test and the corrections perform similar. A real-data application is also presented to illustrate the use of our proposed methods.