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February 2021 A general expression for second-order covariance matrices—an application to dispersion models
Tiago M. Magalhães, Denise A. Botter, Mônica C. Sandoval
Braz. J. Probab. Stat. 35(1): 37-49 (February 2021). DOI: 10.1214/20-BJPS489

Abstract

We present a general expression that allows the calculation of both the $n^{-2}$ asymptotic covariance matrices of the maximum likelihood estimator (MLE) and the first-order bias corrected MLE, where $n$ is the sample size. The formula is presented in a matrix notation which has numerical advantages since it requires only simple operations on matrices and vectors. The usefulness of the formula is to construct better Wald statistics. We apply our findings to dispersion models and develop simulation studies which show that modification in the Wald statistic effectively removes size distortions of the type I error probability with no power loss. For illustrative purposes, a real data application is considered to support our theoretical results.

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Tiago M. Magalhães. Denise A. Botter. Mônica C. Sandoval. "A general expression for second-order covariance matrices—an application to dispersion models." Braz. J. Probab. Stat. 35 (1) 37 - 49, February 2021. https://doi.org/10.1214/20-BJPS489

Information

Received: 1 October 2019; Accepted: 1 September 2020; Published: February 2021
First available in Project Euclid: 6 January 2021

MathSciNet: MR4195758
Digital Object Identifier: 10.1214/20-BJPS489

Rights: Copyright © 2021 Brazilian Statistical Association

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Vol.35 • No. 1 • February 2021
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