Journal Article Measures of multivariate skewness and kurtosis with applications Get access K. V. MARDIA University Hull Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 57, Issue 3, December 1970, Pages 519–530, https://doi.org/10.1093/biomet/57.3.519 Published: 01 1970 history Revision received: March Received:

Journal Article Maximum likelihood estimation of models for residual covariance in spatial regression Get access K. V. MARDIA, MARDIA Department Statistics, University LeedsU.K. Search other works by this author on: Oxford Academic Google Scholar R. J. MARSHALL Biometrika, Volume 71, Issue 1, April 1984, Pages 135–146, https://doi.org/10.1093/biomet/71.1.135 Published: 01 1984 history Received: March 1982 Revision received: June 1983

Summary Directional data analysis is emerging as an important area of statistics. Within the past two decades, various new techniques have appeared, mostly to meet needs scientific workers dealing with directional data. The paper first introduces basic models for multi-dimensional case known von Mises–Fisher distribution and Bingham distribution. Their sampling theory depends heavily on isotropic some developments are discussed. An optimum property test established. A non-parametric proposed...

SUMMARY This paper formulates the problem of measuring bilateral symmetry objects analytically for landmark data, and develops various new testing procedures exploratory data analyses. The development is linked with fundamental biological directional asymmetry fluctuating asymmetry. We distinguish two types symmetry, object matching provide tests under assumptions isotropic variability as well non-isotropy. require novel statistical geometrical analyses Procrustes shape manifold. For...

Summary When n distinguishable directions in p dimensions are required to describe each orientation, Downs (1972) has extended the von Mises–Fisher distribution. We obtain normalizing constant which leads investigation of various basic properties In particular, an explicit expression for first population moment as well asymptotic distribution statistics provided. The estimation problem, important testing problems, and exact sampling distributions dealt with, some techniques applied a set...

Several model-based algorithms for threshold selection are presented, concentrating on the two-population univariate case in which an image contains object and background. It is shown how main ideas behind two important nonspatial thresholding follow from classical discriminant analysis. Novel that make use of available local/spatial information then given. found algorithm using alternating mean median filtering provides acceptable method when relatively highly contaminated, seems to depend...

The effect of nonnormality on multivariate regression tests, the one-way analysis variance and tests equality covariance matrices is studied following approach Box & Watson (1962). In nonnormal case, an approximation to distribution a generalized Mahalanobis distance type statistic for problem derived. It shown that sensitivity in observations determined by extent regressors. randomization deduced. found be robust whereas are sensitive nonnormality. An explanation this varying degree given.

Consider a sequence of, say, 10 to 20 vector observations in three-dimensional space. It is suspected that few subsets of consecutive are made up collinear points. The purpose this paper construct statistically based algorithm find such linear segments and assess their accuracy. A similar assessment for coplanar sets This applied here palaeomagnetic data claimed be superior previous methods analysis terms completeness balance analysis, treatment measurement errors other sources scatter,...

A fundamental problem in bioinformatics is to characterize the secondary structure of a protein, which has traditionally been carried out by examining scatterplot (Ramachandran plot) conformational angles. We examine two natural bivariate von Mises distributions--referred as Sine and Cosine models--which have five parameters and, for concentrated data, tend normal distribution. These are analyzed their main properties derived. Conditions on established result bimodal behavior joint density...

Despite significant progress in recent years, protein structure prediction maintains its status as one of the prime unsolved problems computational biology. One key remaining challenges is an efficient probabilistic exploration structural space that correctly reflects relative conformational stabilities. Here, we present a fully probabilistic, continuous model local atomic detail. The generative makes sampling possible and provides framework for rigorous analysis sequence–structure...

Abstract The paper gives a new optimal property of the classical method multi-dimensional scaling when distance matrix is non-Euclidean. We also examine robustness under linear model. A technique to estimate missing values given. Keywords: solutionprincipal coordinateseuclidean representationlinear modelmissing