A Nonparametric Test of Independence Between Two Sets of Random Variables and Tests of Normality in Multivariate DataCornell University, 1991 - 256 pages |
Common terms and phrases
5000 iterations asymptotically equivalent Cell Numbers central limit theorem Chi-square Percentile Percentile Comparison between Empirical covariance matrix Cramér-von Mises type Csörgő denote distribution function dtin empirical characteristic function empirical characteristic process Empirical Chi-square Percentile empirical distribution function Empirical Powers exp(itZ Əsm fn(Ž Gaussian process H₁ increases Independence against Alternatives j=1 kn+1 mn joint pdf kın kn mn kn mn-1 kn+1 mn i=1 knln Lemma log log log Pij lognormal mn-1 kn Multivariate Normality Test n*pij Zij Normal Distribution number of cells order statistics p-variate Percent Empirical Chi-square Percentile Empirical Pi,mn Pij Zij Pkn+1 Pkn+1,mn power power power powers in percentage proof proposed test random variables result rlin Rn(j S₂ sl2n stochastic process Table Test of Independence test statistic underlying distribution vectors w(n*pij weak convergence weight(w Yn(t Zi,mn Zkn+1,j Σ Σ ΣΣ