New Invariant and Consistent Chi-squared Type Goodness-of-fit Tests for Multivariate Normality and a Related Comparative Simulation Study

• Activity Number: 82
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Vassiliy Voinov*+ and Natalie Pya and Rashid Makarov and Yevgeniy Voinov
• Companies: KIMEP University and KIMEP University and KIMEP University and KIMEP University
• Keywords: Chi-squared goodness-of-fit tests ; invariant and consistent tests ; multivariate normality ; symmetric alternatives ; power of tests

Abstract

New chi-squared type invariant and consistent goodness-of-fit tests for multivariate normality are introduced. The tests are based on the Karhunen-Loève transformation of a multi-dimensional sample from a population. This transformation diagonalizes the sample covariance matrix. Then a modification of Moore and Stubblebine technique for construction Wald's type chi-squared tests was used. A comparison of simulated powers of these tests and some other well known tests with respect to seven different symmetrical multivariate alternatives is given. The simulation study demonstrates that the power of the proposed McCull test almost does not depend on the number of grouping cells. The test shows an advantage over other chi-squared type tests and is more powerful than several known tests against some alternatives.