Abstract
A bewildering large number of test statistics have been found for testing the presence of an outlier in multiple linear regression models. Exact critical values of these test statistics are not available, and approximate ones are usually obtained by the first-order Bonferroni upper bound or large-scale simulations. In this paper, we show that the upper bound values of two of these test statistics are algebraically the same. An application to real data for multiple linear regression is used to demonstrate the procedure.
Highlights
Upper bounds for the critical values of test statistics for detecting the presence of a single outlier in linear regression have been developed by [7, 8]
Formal distinctions exist in the principles invoked by [7, 8] in deriving these upper bounds, we show in this paper that these upper bounds derived by [7, 8] are algebraically the same
Numerous graphical and numerical techniques for checking model assumptions using standardized residuals can be found in the regression literature. They are fundamental building blocks for most of the known test statistics studied in the literature for outlier detection in linear models
Summary
Outliers usually have a major influence on the resulting parameter estimates, and their presence impacts adversely on the results of the statistical inference concerning the models. Upper bounds for the critical values of test statistics for detecting the presence of a single outlier in linear regression have been developed by [7, 8]. Numerous graphical and numerical techniques for checking model assumptions using standardized residuals can be found in the regression literature They are fundamental building blocks for most of the known test statistics studied in the literature for outlier detection in linear models (see [9, 10]). Reference [11], following the suggestion of [12], used a large-scale simulation study involving many thousands of sampling experiments to obtain approximate critical values of (7) for a simple linear regression.
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