2015/02/19 by Ana M. Bianco, Bianco, Ana M., Graciela Boente +3
Mathematics · Environmental Science · #Advanced Statistical Methods and Models #Statistical Methods and Inference #Soil Geostatistics and Mapping
paper · pdf · doi:10.48550/arxiv.1502.05600
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions that include elliptical distributions without first moments, we derive the test statistic asymptotic behaviour under the null hypothesis and under special alternatives. Numerical experiments allow to compare the behaviour of the tests based on the sample mean and covariance matrix with that based on robust estimators, under various elliptical distributions and different alternatives. This comparison was done looking not only at the observed level and power but we rather use the size-corrected relative exact power which provides a tool to assess the test statistic skill to detect alternatives. We also provide a numerical comparison with other competing tests.