# The Open Mathematics, Statistics and Probability Journal

The Open Statistics & Probability Journal

(Discontinued)

ISSN: 2666-1489 ― Volume 10, 2020
RESEARCH ARTICLE

# Asymptotic Relative Efficiencies of the Score and Robust Tests in Genetic Association Studies

Ao Yuan1, *, Ruzong Fan1, Jinfeng Xu2, Yuan Xue3, Qizhai Li4
1 Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington DC, 20057, USA
2 Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong
3 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
4 LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

## Abstract

### Introduction:

The score statistic Z(θ) and the maximin efficient robust test statistic ZMERT are commonly used in genetic association study, but according to our knowledge there is no formal comparison of them.

### Methods:

In this report, we compare the asymptotic behavior of Z(θ) and ZMERT, by computing their Asymptotic Relative Efficiencies (AREs) relative to each other. Four commonly used ARE measures, the Pitman ARE, Chernoff ARE, Hodges-Lehmann ARE and the Bahadur ARE are considered. Some modifications of these methods are made to simplify the computations. We found that the Chernoff, Hodges-Lehmann and Bahadur AREs are suitable for our setting.

### Results and Conclusion:

Based on our study, the efficiencies of the two test statistic varies for different criterion used, and for different parameter values under the same criterion, so each test has its advantages and dis-advantages according to the criterion used and the parameters involved, which are described in the context. Numerical examples are given to illustrate the use of the two statistics in genetic association study.

Keywords: Asymptotic relative efficiency, Genetic association study, Maximin efficiency robust test, Score test Z(θ), Test statistic Zmert, Pitman ARE, Chernoff ARE.

### Article Information

#### Identifiers and Pagination:

Year: 2018
Volume: 9
First Page: 26
Last Page: 41
Publisher Id: TOSPJ-9-26
DOI: 10.2174/1876527001809010026

#### Article History:

Acceptance Date: 2/10/2018
Electronic publication date: 28/12/2018
Collection year: 2018

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington DC, 20057, USA, Tel: +91 22 33611111, E-mail: ay312@georgetown.edu

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