Kanti V. Mardia

Bio: Kanti V. Mardia is an academic researcher from University of Leeds. The author has contributed to research in topics: Shape analysis (digital geometry) & von Mises distribution. The author has an hindex of 54, co-authored 235 publications receiving 20393 citations. Previous affiliations of Kanti V. Mardia include Indian Institute of Management Ahmedabad & Newcastle University.

Measures of multivariate skewness and kurtosis with applications

Abstract: SUMMARY Measures of multivariate skewness and kurtosis are developed by extending certain studies on robustness of the t statistic. These measures are shown to possess desirable properties. The asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test of multivariate normality is proposed. The effect of nonnormality on the size of the one-sample Hotelling's T2 test is studied empirically with the help of these measures, and it is found that Hotelling's T2 test is more sensitive to the measure of skewness than to the measure of kurtosis. measures have proved useful (i) in selecting a member of a family such as from the Karl Pearson family, (ii) in developing a test of normality, and (iii) in investigating the robustness of the standard normal theory procedures. The role of the tests of normality in modern statistics has recently been summarized by Shapiro & Wilk (1965). With these applications in mind for the multivariate situations, we propose measures of multivariate skewness and kurtosis. These measures of skewness and kurtosis are developed naturally by extending certain aspects of some robustness studies for the t statistic which involve I1 and 32. It should be noted that measures of multivariate dispersion have been available for quite some time (Wilks, 1932, 1960; Hotelling, 1951). We deal with the measure of skewness in ? 2 and with the measure of kurtosis in ? 3. In ? 4 we give two important applications of these measures, namely, a test of multivariate normality and a study of the effect of nonnormality on the size of the one-sample Hotelling's T2 test. Both of these problems have attracted attention recently. The first problem has been treated by Wagle (1968) and Day (1969) and the second by Arnold (1964), but our approach differs from theirs.

Statistical Shape Analysis: With Applications in R

Abstract: Preliminaries: Size Measures and Shape Coordinates. Preliminaries: Planar Procrustes Analysis. Shape Space and Distance. General Procrustes Methods. Shape Models for Two Dimensional Data. Tangent Space Inference. Size--and--Shape. Distributions for Higher Dimensions. Deformations and Describing Shape Change. Shape in Images. Additional Topics. References and Author Index. Index.

Maximum likelihood estimation of models for residual covariance in spatial regression

Abstract: We describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters. Observations are assumed to be Gaussian. We give conditions which ensure consistency and asymptotic normality of the estimators. Our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators. We also discuss an application of the spectral approximation to the likelihood for processes on a lattice.

A new method for non-parametric multivariate analysis of variance

Abstract: Hypothesis-testing methods for multivariate data are needed to make rigorous probability statements about the effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, however, are too stringent in their assumptions for most ecological multivariate data sets. Non-parametric methods, based on permutation tests, are preferable. This paper describes a new non-parametric method for multivariate analysis of variance, after McArdle and Anderson (in press). It is given here, with several applications in ecology, to provide an alternative and perhaps more intuitive formulation for ANOVA (based on sums of squared distances) to complement the description pro- vided by McArdle and Anderson (in press) for the analysis of any linear model. It is an improvement on previous non-parametric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lack of formal assumptions of other non-parametric methods. The test- statistic is a multivariate analogue to Fisher's F-ratio and is calculated directly from any symmetric distance or dissimilarity matrix. P-values are then obtained using permutations. Some examples of the method are given for tests involving several factors, including factorial and hierarchical (nested) designs and tests of interactions.

Spatial Econometrics: Methods and Models

Abstract: 1: Introduction.- 2: The Scope of Spatial Econometrics.- 3: The Formal Expression of Spatial Effects.- 4: A Typology of Spatial Econometric Models.- 5: Spatial Stochastic Processes: Terminology and General Properties.- 6: The Maximum Likelihood Approach to Spatial Process Models.- 7: Alternative Approaches to Inference in Spatial Process Models.- 8: Spatial Dependence in Regression Error Terms.- 9: Spatial Heterogeneity.- 10: Models in Space and Time.- 11: Problem Areas in Estimation and Testing for Spatial Process Models.- 12: Operational Issues and Empirical Applications.- 13: Model Validation and Specification Tests in Spatial Econometric Models.- 14: Model Selection in Spatial Econometric Models.- 15: Conclusions.- References.