Journal of Advanced Statistics

6

Authors: Deepa R. Acharya, Parameshwar V. Pandit

Nonparametric tests for location problems have received much attention in the literature. Many nonparametric tests have been proposed for one, two and several samples location problems. In this paper a class of test statistics is proposed for two sample location problem when the underlying distributions of the samples are symmetric. The class of test statistics proposed is linear combination of U-statistics whose kernel is based on subsamples extrema. The members of the new class are shown to be asymptotically normal. The performance of the proposed class of tests is evaluated using Pitman Asymptotic Relative Efficiency. It is observed that the members of the proposed class of tests are better than the existing tests in the literature.

8

Authors: Kanchan Jain, Bhavna Kaushal, Suresh K. Sharma

Receiver Operating Characteristic (ROC) curves are used for evaluation of classifier’s performance. They have applications in clinical diagnostics in medicine, computational linguistics, machine learning and data mining. In this paper, we propose a test for the equality of two ROC curves for Bi-Pareto ROC model. The asymptotic distribution of the test statistic is determined through simulations and the size of the test is computed. A real data set has been used to demonstrate the testing procedure.

16

Authors: Shengning Xiao, Jin-Ting Zhang

In this article we consider testing for main and interaction effects in heteroscedastic two-way MANOVA model. We express the model in the form of the general linear hypothesis testing (GLHT) problem and construct the sum of squares and cross products (SSCP) matrices due to hypothesis and error respectively. We modify the classical Wilks’s Likelihood Ratio (WLR), Lawley-Hotelling Trace (LHT) and Bartlett-Nanda-Pillai trace (BNP) tests based on these two SSCP matrices with the approximate degrees of freedoms (ADF) obtained by matching the means and the total variations of the SSCP matrices and their respective approximating Wishart distributions. The resulting modified WLR, LHT, BNP tests are shown to be invariant under affine-transformations, different choices of the contrast matrix used to define the same hypothesis, and different labeling schemes of the cell mean vectors. Simulation studies presented in this paper also show that the proposed tests generally perform well and outperform one existing approach in terms of controlling the desired size and enhancing the powers. An example from a Smoking Cessation trial is given to illustrate the proposed methodologies.