.png)
12 – International Efforts in Statistical Capacity Building: How You Can Help
New Invariant and Consistent Chi-squared Type Goodness-of-fit Tests for Multivariate Normality and a Related Comparative Simulation Study
Vassiliy Voinov
KIMEP University
Natalie Pya
KIMEP University
Rashid Makarov
KIMEP University
Yevgeniy Voinov
KIMEP University
`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.