Summary
A family of statistics is presented that can be used for testing goodness of fit to a parametric family. These statistics include Mardia's measure of multivariate kurtosis and Moore and Stubblebine's test for multivariate normality. The asymptotic distribution of the statistics is found under mild hypotheses on the parametric family and, in the case of multivariate normality, the distribution is shown to be independent of the “true” parameter. A class of tests for multivariate normality is presented and the performance of two such tests in the bivariate case is found in simulations.
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The research of this author was carried out in part while at M.I.T. and then at Bell Communications Research
The research of this author was partially supported by National Science Foundation Grants
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Quiroz, A.J., Dudley, R.M. Some new tests for multivariate normality. Probab. Th. Rel. Fields 87, 521–546 (1991). https://doi.org/10.1007/BF01304278
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DOI: https://doi.org/10.1007/BF01304278
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Asymptotic Distribution
- Parametric Family