Semiparametrically efficient rank-based inference for shape. II. Optimal R-estimation of shape

Semiparametrically Efficient Rank - Based Inference for Shape Ii . Optimal R - Estimation of Shape

A class of R-estimators based on the concepts of multivariate signed ranks and the optimal rank-based tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical distribution. These R-estimators are root-n consistent under any radial density g, without any moment assumptions, and semiparametrically efficient at some pre...

Semiparametrically Efficient Rank-based Inference for Shape I. Optimal Rank-based Tests for Sphericity

We propose a class of rank-based procedures for testing that the shape matrix V of an elliptical distribution (with unspecified center of symmetry, scale, and radial density) has some fixed value V0; this includes, for V0 = Ik, the problem of testing for sphericity as an important particular case. The proposed tests are invariant under translations, monotone radial transformations, rotations, a...

Efficient Statistical Methods for 3D Shape Inference

Visual inference is a complex and ambiguous problem, and these properties have presented a significant obstacle to developing effective algorithms for many visual tasks. In this thesis, I begin by developing a methodology for statistical inference that is particularly suited for the complex tasks of visual perception. The approach is based on Belief Propagation, a highly successful inference te...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Optimal Shape Design for a Cooling Pin Fin Connection Profil

A shape optimization problem of cooling fins for computer parts and integrated circuits is modeled and solved in this paper. The main purpose is to determine the shape of a two-dimensional pin fin, which leads to the maximum amount of removed heat. To do this, the shape optimization problem is defined as maximizing the norm of the Nusselt number distribution at the boundary of the pin fin's con...