Matrix-Variate Discriminative Analysis, Integrative Hypothesis Testing, and Geno-Pheno A5 Analyzer

Abstract. A general perspective is provided on both on hypothesis testing and discriminative analyses, by which matrix-variate discriminative analyses are pro-posed based on the matrix normal distribution, featured by a bi-linear extension of Fisher linear discriminant analysis and a further extension to binary variables. Moreover, a general formulation is proposed for integrative hypothesis testing and five typical categories are summarized. Furthermore, major techniques for varia-ble selection are briefly elaborated. Finally, taking analyses of gene expression and exome sequencing as examples, we further propose a general procedure called Geno-Pheno A5 Analyzer for integrative discriminant analysis

Linear statistics and exponential families

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A test for uniformity with unknown limits based on d'agostino's D

Although still being recommended as a goodness-of-fit test for normality, we present some motivations to consider D'Agostino's statistic D for testing of uniformity on an unknown interval. As a matter of fact, D turns out to be a linear function of the Cramer-von Mises distance between the empirical distribution function and a rectangular distribution with suitably estimated endpoints. The limiting null distribution of D is found.D'Agostino's D test for uniformity with unknown limits U-statistics characterization of the uniform distribution

A new weighted integral goodness-of-fit statistic for exponentiality

We propose a new weighted integral goodness-of-fit statistic for exponentiality. The statistic is motivated by a characterization of the exponential distribution via the mean residual life function. Its limit null distribution is the same as that of a certain weighted integral of the squared Brownian bridge. The Laplace transform and cumulants of the latter are expressible in terms of Bessel functions.

A goodness of fit test for the Poisson distribution based on the empirical generating function

The generating function g(t) of the Poisson distribution with parameter [lambda] is the only generating function satisfying the differential equation g'(t) = [lambda]g(t). Denoting by gn(t) the empirical generating function of a random sample X1,..., Xn of size n drawn from a distribution concentrated on the nonnegative integers, we propose Tn = n[integral operator]01[n(t)- g'n(t)]2 dt as a goodness of fit statistic for the composite hypothesis that the distribution of Xi is Poisson. Using a parametric bootstrap to have a critical value, and estimating this in turn by Monte Carlo the resulting test is shown to be consistent against alternative distributions with finite expectation.Poisson distribution goodness of fit empirical generating function bootstrapping Monte Carlo samples

On a new multivariate two-sample test

In this paper we propose a new test for the multivariate two-sample problem. The test statistic is the difference of the sum of all the Euclidean interpoint distances between the random variables from the two different samples and one-half of the two corresponding sums of distances of the variables within the same sample. The asymptotic null distribution of the test statistic is derived using the projection method and shown to be the limit of the bootstrap distribution. A simulation study includes the comparison of univariate and multivariate normal distributions for location and dispersion alternatives. For normal location alternatives the new test is shown to have power similar to that of the t- and T2-Test.Multivariate two-sample test Bootstrapping Projection method Orthogonal invariance Cramer test