Robust Wilks' Statistic based on RMCD for One-Way Multivariate Analysis of Variance (MANOVA)

The classical Wilks' statistic is the most using for testing the hypotheses of equal mean vectors of several multivariate normal populations for one-way MANOVA. It is extremely sensitive to the influence of outliers. Therefore, the robust Wilks' statistic based on reweighted minimum covariance determinant (RMCD) estimator with Hampel weighted function has been proposed. The distribution of the proposed statistic differs from the classical one. Mont Carlo simulations are used to evaluate the performance of the test statistic under the normal and contaminated distribution for the data set. Moreover, the type I error rate and power of test have been considered as statistical measures to comparison between the classical and the robust statistics. The results show that, the robust Wilks' statistic based on RMCD is closely to the classical Wilks' statistic in case of normal distribution for the data set while in case of contaminated distribution the method in question is the best. Keywords: One-Way Multivariate Analysis of Variance, Wilks' Statistic, Outliers, Robustness, Minimum Covariance Determinant Estimator.

MATS: Inference for potentially Singular and Heteroscedastic MANOVA

In many experiments in the life sciences, several endpoints are recorded per subject. The analysis of such multivariate data is usually based on MANOVA models assuming multivariate normality and covariance homogeneity. These assumptions, however, are often not met in practice. Furthermore, test statistics should be invariant under scale transformations of the data, since the endpoints may be measured on different scales. In the context of high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test statistic for a specific one-way model, which, however, relies on the assumption of a common non-singular covariance matrix. We modify and extend this test statistic to factorial MANOVA designs, incorporating general heteroscedastic models. In particular, our only distributional assumption is the existence of the group-wise covariance matrices, which may even be singular. We base inference on quantiles of resampling distributions, and derive confidence regions and ellipsoids based on these quantiles. In a simulation study, we extensively analyze the behavior of these procedures. Finally, the methods are applied to a data set containing information on the 2016 presidential elections in the USA with unequal and singular empirical covariance matrices

DISCO analysis: A nonparametric extension of analysis of variance

In classical analysis of variance, dispersion is measured by considering squared distances of sample elements from the sample mean. We consider a measure of dispersion for univariate or multivariate response based on all pairwise distances between-sample elements, and derive an analogous distance components (DISCO) decomposition for powers of distance in $(0,2]$. The ANOVA F statistic is obtained when the index (exponent) is 2. For each index in $(0,2)$, this decomposition determines a nonparametric test for the multi-sample hypothesis of equal distributions that is statistically consistent against general alternatives.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS245 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Automatic Classification and Speaker Identification of African Elephant (\u3cem\u3eLoxodonta africana\u3c/em\u3e) Vocalizations

A hidden Markov model (HMM) system is presented for automatically classifying African elephant vocalizations. The development of the system is motivated by successful models from human speech analysis and recognition. Classification features include frequency-shifted Mel-frequency cepstral coefficients (MFCCs) and log energy, spectrally motivated features which are commonly used in human speech processing. Experiments, including vocalization type classification and speaker identification, are performed on vocalizations collected from captive elephants in a naturalistic environment. The system classified vocalizations with accuracies of 94.3% and 82.5% for type classification and speaker identification classification experiments, respectively. Classification accuracy, statistical significance tests on the model parameters, and qualitative analysis support the effectiveness and robustness of this approach for vocalization analysis in nonhuman species

SAS/IML Macros for a Multivariate Analysis of Variance Based on Spatial Signs

Recently, new nonparametric multivariate extensions of the univariate sign methods have been proposed. Randles (2000) introduced an affine invariant multivariate sign test for the multivariate location problem. Later on, Hettmansperger and Randles (2002) considered an affine equivariant multivariate median corresponding to this test. The new methods have promising efficiency and robustness properties. In this paper, we review these developments and compare them with the classical multivariate analysis of variance model. A new SAS/IML tool for performing a spatial sign based multivariate analysis of variance is introduced.

Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear Models: SAS Software and Examples

This paper describes graphical methods for multiple-response data within the framework of the multivariate linear model (MLM), aimed at understanding what is being tested in a multivariate test, and how factor/predictor effects are expressed across multiple response measures. In particular, we describe and illustrate a collection of SAS macro programs for: (a) Data ellipses and low-rank biplots for multivariate data, (b) HE plots, showing the hypothesis and error covariance matrices for a given pair of responses, and a given effect, (c) HE plot matrices, showing all pairwise HE plots, and (d) low-rank analogs of HE plots, showing all observations, group means, and their relations to the response variables.