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

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.

R. Douglas Martin
,
Chindhanai Uthaisaad
,
Daniel Z. Xia

2020-09-10

## Supplementary materials

Supplementary materials are available in addition to this article. It can be downloaded at
RJ-2020-019.zip

## CRAN packages used

sn

## CRAN Task Views implied by cited packages

Distributions, Multivariate

### Reuse

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### Citation

For attribution, please cite this work as

Martin, et al., "The R Journal: Skew-t Expected Information Matrix Evaluation and Use for Standard Error Calculations", The R Journal, 2020

BibTeX citation

@article{RJ-2020-019,
author = {Martin, R. Douglas and Uthaisaad, Chindhanai and Xia, Daniel Z.},
title = {The R Journal: Skew-t Expected Information Matrix Evaluation and Use for Standard Error Calculations},
journal = {The R Journal},
year = {2020},
note = {https://doi.org/10.32614/RJ-2020-019},
doi = {10.32614/RJ-2020-019},
volume = {12},
issue = {1},
issn = {2073-4859},
pages = {188-205}
}