A Wald's-Type Goodness-of-Fit Test for Binormality

• 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): Yevgeniy Voinov*+
• Companies: KIMEP University
• Keywords: Binormality ; chi-squared goodness-of-fit test ; invariant tests ; power of tests

Abstract

A new Wald's type chi-squared invariant goodness-of-fit test for binormality is introduced. The test is based on a linear transformation of a two-dimensional sample from a population that diagonalizes the sample covariance matrix, and a modification of Moore and Stubblebine technique for construction chi-squared type tests proposed in 1981. More precise formulation of the well known Moore's 1977 theorem given by Voinov in 2013 permitted to get this new result. A comparison of simulated power of the test with respect to numerous alternatives is presented. The simulated power of the proposed modified McCulloch's test with respect to nine different alternatives is comparable with the power of the well-known Anderson-Darling, Cramer-von Mises, Henze and Zirkler , Doornik and Hansen, and, modified by Royston in 1992, the Shapiro-Wilk's W tests. The overall conclusion of this research is that all seven tests considered can be used in practice.