Nonparametric and Robust Methods for Multivariate and Functional Data


The goal of this project is to do world class basic research in developing new nonparametric and robust statistical methods for high-dimensional and functional data with biometrical applications and applications in statistical signal processing.

Motivation

Classical multivariate statistical methods (MANOVA, PCA, multivariate multiple regression, canonical correlation analysis, factor analysis, etc.) are based on the mean vector and sample covariance matrix. The regular mean vector and sample covariance matrix and consequently the standard multivariate techniques based on these are, however, highly sensitive to outlying observations and heavy tailed noise distribution. In this work new nonparametric and robust techniques are derived for these multivariate and functional inference problems.

Aim of the research

Robust and nonparametric competitors to the standard normal theory based multivariate inference methods and analysis tools for high-dimensional data are developed. The procedures are optimal in the semiparametric elliptic and independent component (IC) models. The estimates and tests are often based on different multivariate concepts of sign and rank. The statistical properties of the new robust estimates and tests (large and small sample properties, equivariance, efficiency, robustness, etc.) are found. Computationally efficient algorithms (R pacakages) will be developed.

The new techniques, including robust ICA, supervised and unsupervised dimension reduction, are applied to different high-dimensional data analysis problems in cooperation with other research groups (signal processing, gene expression data, nutritional data, rainfall data, school health data, etc.).

Subprojects

Researchers and co-operators in Finland, 1998-

Doctoral Theses

Cooperation