Abstract
We propose a visual test of goodness of fit for families of elliptically symmetric distributions based on a test statistic derived from scale–scale plots. The scale–scale plots are constructed based on the volume functionals of the central rank regions. The test is motivated through the multivariate normal distributions and extended to a test of elliptical symmetry. We derive the asymptotic properties of the test statistic, and we perform detailed power studies for the test of goodness of fit, as well as the test for elliptical symmetry. We also compare the performance of the proposed test with some well-known alternatives.
| Original language | English |
|---|---|
| Article number | e319 |
| Number of pages | 14 |
| Journal | Stat |
| Volume | 10 |
| Issue number | 1 |
| Early online date | 24 Sept 2020 |
| DOIs | |
| Publication status | Published - Dec 2021 |
Bibliographical note
Funding Information:This work is part of the first author's PhD thesis under the guidance of the second author. The thesis was completed at the School of Mathematics, University of Birmingham, UK. The authors would also like to thank the associate editor and two anonymous referees for their helpful suggestions. The authors are also grateful to Dr Pinakpani Pal, Indian Statistical Institute, Calcutta, for his suggestions in stable implementation of the codes.
Publisher Copyright:
© 2020 John Wiley & Sons, Ltd.
Keywords
- affine invariance
- elliptical symmetry
- rank regions
- scale–scale plot
- slope functional
- volume functional
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty