Skew-t Expected Information Matrix Evaluation and Use for Standard Error Calculations

Authors

• R. Douglas Martin, University of Washington
• Chindhanai Uthaisaad, University of Washington
• Daniel Z. Xia, University of Washington

Date of this Version

6-2020

Document Type

Article

Citation

The R Journal (June 2020) 12(1); Editor: Michael J. Kane

Comments

Copyright 2020, The R Foundation. Open access material. License: CC BY 4.0 International

Abstract

Skew-t distributions derived from skew-normal distributions, as developed by Azzalini and several co-workers, are popular because of their theoretical foundation and the availability of computational methods in the R package sn. One difficulty with this skew-t family is that the elements of the expected information matrix do not have closed form analytic formulas. Thus, we developed a numerical integration method of computing the expected information matrix in the R package skewtInfo. The accuracy of our expected information matrix calculation method was confirmed by comparing the result with that obtained using an observed information matrix for a very large sample size. A Monte Carlo study to evaluate the accuracy of the standard errors obtained with our expected information matrix calculation method, for the case of three realistic skew-t parameter vectors, indicates that use of the expected information matrix results in standard errors as accurate as, and sometimes a little more accurate than, use of an observed information matrix.