Robust Tests for Spherical Symmetry and Their Application to Least Squares Regression
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In this article, it was shown that Kariya and Eaton's test for multivariate spherical symmetry is UMP invariant against elliptically symmetric distributions and that both the null and alternative distributions of the test statistic are the same as those which occur when the sample is normally distributed.Abstract:
Invariance is used to show that Kariya and Eaton's test for multivariate spherical symmetry is UMP invariant against elliptically symmetric distributions. Also both the null and alternative distributions of the test statistic are found to be the same as those which occur when the sample is normally distributed. UMP and UMPU tests for serial correlation derived assuming normality are found to be even more robust against departure from this assumption than was recently demonstrated by Kariya. When applied to the linear regression model, these results give useful robustness properties for Kadiyala's $T1$ test and the Durbin-Watson test.read more
Citations
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References
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Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.
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Journal ArticleDOI
Testing for serial correlation in least squares regression. II.
James Durbin,G. S. Watson +1 more
TL;DR: The problem of testing the errors for independence forms the subject of this paper and its successor and deals mainly with the theory on which the test is based, while the second paper describes the test procedures in detail and gives tables of bounds to the significance points of the test criterion adopted.
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TL;DR: In this paper, a self-contained account of linear least squares when the errors have an arbitrary error covariance matrix, bringing together the distinct literatures of analysis of variance and time series analysis, is given.