Inference for Mean Directions of Several Circular and Spherical Distributions

Event Date: 

Wednesday, May 7, 2014 - 3:30pm to 5:00pm

Event Date Details: 

Refreshments served at 3:15 PM

Event Location: 

  • South Hall 5607F

Dr. Ashis SenGupta (University of California, Riverisde & Applied Statistics Unit, Indian Statistical Institute, Kolkata)

Title: Inference for Mean Directions of Several Circular and Spherical Distributions

Abstract: The problems of decision theoretic estimation and testing of homogeneity of mean directions of several independent circular and spherical distributions are considered. First, admissibility, minimaxity and some other decision theoretic properties of the MLEs of several independent Langevin distributions are studied. Then, the problem of testing of homogeneity of the mean direction parameters is taken up. Probability distributions enhanced for modeling directional data do not in general have scale parameters, but have concentration parameters which play a role inverse to that of a scale parameter for distributions for linear data. The absence of invariant statistic with respect to that of the concentration parameter leads to difficulties in deriving optimal tests in their presence as nuisance parameters. However, parameter orthogonality may still exist in such distributions. First, the structure of Dispersion Model for some circular distributions is exposed and exploited to construct the relevant tests. Then for the case of nuisance concentration parameters, the theory of Integrated Likelihood based tests is extended to derive optimal test for the stated problem. Generalization of the above approach from the circular to the spherical case is presented next. Several real-life examples are presented to illustrate our approach.