Mathematics and Statistics Vol. 9(6), pp. 1004 - 1010
DOI: 10.13189/ms.2021.090616
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An Asymptotic Test for A Single Outlier in Linear Regression Models

Ugah Tobias Ejiofor ¹, Mba Emmanuel Ikechukwu ^1,*, Eze Micheal Chinonso ¹, Arum Kingsley Chinedu ¹, Mba Ifeoma Christy ², Urama Chinasa ², Comfort Njideka Ekene-Okafor ^3
1 Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Enugu State, Nigeria
² Department of Economics, Faculty of Social Sciences, University of Nigeria, Nsukka, Enugu State, Nigeria
³ Department of Computer Sciences/Mathematics, Faculty of Natural Sciences and Environmental Studies, Godfrey Okoye University, Enugu State, Nigeria

ABSTRACT

It is not uncommon to find an outlier in the response variable in linear regression. Such a deviant value needs to be detected and scrutinized to find out why it is not in agreement with its fitted value. Srikantan [1] has developed a test statistic for detecting the presence of an outlier in the response variable in a multiple linear regression model. Approximate critical values of this test statistic are available and are obtained based on the first-order Bonferroni upper bound. The exact critical values are not available and a result of that, tests carried out on the basis of this approximate critical values may not be very accurate. In this paper, we obtained more accurate and precise critical values of this test statistic for large sample sizes (herein called asymptotic critical values) to improve on the tests that use these critical values. The procedure involved using the exact probability density function of this test statistic to obtain its asymptotic critical values. We then compared these asymptotic critical values with the approximate critical values obtained. An application to simulation results for linear regression models was used to examine the power of this test statistic. The asymptotic critical values obtained were found to be more accurate and precise. Also, the test performed better under these asymptotic values (the power performance of this test statistic was found to better when the asymptotic critical values were used).

KEYWORDS
Asymptotic, Bonferroni upper Bound, Critical Values, Internally Studentized Residuals, Outlier, Regression, Residual, Test Statistic

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ugah Tobias Ejiofor , Mba Emmanuel Ikechukwu , Eze Micheal Chinonso , Arum Kingsley Chinedu , Mba Ifeoma Christy , Urama Chinasa , Comfort Njideka Ekene-Okafor , "An Asymptotic Test for A Single Outlier in Linear Regression Models," Mathematics and Statistics, Vol. 9, No. 6, pp. 1004 - 1010, 2021. DOI: 10.13189/ms.2021.090616.

(b). APA Format:
Ugah Tobias Ejiofor , Mba Emmanuel Ikechukwu , Eze Micheal Chinonso , Arum Kingsley Chinedu , Mba Ifeoma Christy , Urama Chinasa , Comfort Njideka Ekene-Okafor (2021). An Asymptotic Test for A Single Outlier in Linear Regression Models. Mathematics and Statistics, 9(6), 1004 - 1010. DOI: 10.13189/ms.2021.090616.