Evaluation of the Fourth Millennium Development Goal Realisation Using Robust and Nonparametric Tools Offered by Data Depth Concept

We briefly communicate results of a nonparametric and robust evaluation of effects of \emph{the Fourth Millennium Development Goal of United Nations}. Main aim of the goal was reducing by two thirds, between 1990--2015, the under five months child mortality. Our novel analysis was conducted by means of very powerful and user friendly tools offered by the \emph{Data Depth Concept} being a collection of multivariate techniques basing on multivariate generalizations of quantiles, ranges and order statistics. Results of our analysis are more convincing than results obtained using classical statistical tools.Comment: The paper is basing on a poster submitted to IASC 2014 Data Competition - the poster was the runner-up (the second place

Determination of the Joint Confidence Region of Optimal Operating Conditions in Robust Design by Bootstrap Technique

Robust design has been widely recognized as a leading method in reducing variability and improving quality. Most of the engineering statistics literature mainly focuses on finding "point estimates" of the optimum operating conditions for robust design. Various procedures for calculating point estimates of the optimum operating conditions are considered. Although this point estimation procedure is important for continuous quality improvement, the immediate question is "how accurate are these optimum operating conditions?" The answer for this is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, with the help of the bootstrap technique, we develop procedures for obtaining joint "confidence regions" for the optimum operating conditions. Two different procedures using Bonferroni and multivariate normal approximation are introduced. The proposed methods are illustrated and substantiated using a numerical example.Comment: Two tables, Three figure

Generalized robust shrinkage estimator and its application to STAP detection problem

Recently, in the context of covariance matrix estimation, in order to improve as well as to regularize the performance of the Tyler's estimator [1] also called the Fixed-Point Estimator (FPE) [2], a "shrinkage" fixed-point estimator has been introduced in [3]. First, this work extends the results of [3,4] by giving the general solution of the "shrinkage" fixed-point algorithm. Secondly, by analyzing this solution, called the generalized robust shrinkage estimator, we prove that this solution converges to a unique solution when the shrinkage parameter $\beta$ (losing factor) tends to 0. This solution is exactly the FPE with the trace of its inverse equal to the dimension of the problem. This general result allows one to give another interpretation of the FPE and more generally, on the Maximum Likelihood approach for covariance matrix estimation when constraints are added. Then, some simulations illustrate our theoretical results as well as the way to choose an optimal shrinkage factor. Finally, this work is applied to a Space-Time Adaptive Processing (STAP) detection problem on real STAP data

A subsampling method for the computation of multivariate estimators with high breakdown point

All known robust location and scale estimators with high breakdown point for multivariate sample's are very expensive to compute. In practice, this computation has to be carried out using an approximate subsampling procedure. In this work we describe an alternative subsampling scheme, applicable to both the Stahel-Donoho estimator and the estimator based on the Minimum Volume Ellipsoid, with the property that the number of subsamples required is substantially reduced with respect to the standard subsampling procedures used in both cases. We also discuss some bias and variability properties of the estimator obtained from the proposed subsampling process