Nonparametric and Robust Multivariate Methods

The goal of this project (NRMM) is to do world class basic research in developing new nonparametric and robust statistical methods for high-dimensional and dependent 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 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 mainly 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, 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

MANOVA : One sample, two samples, and several samples multivariate location estimates and tests
PCA, ICS, ICA, SIR: The use of (supervised and unsupervised) scatter matrices in data reduction, in subspace estimation and in searching for independent components
Multivariate regression analysis
CCA: Canonical correlation analysis and tests of independence and conditional independence
Tests for multinormality and tests for ellipticity, tests for the indpendence component model
Hyperplanes and interdirections as tools for multivariate data analysis; the connections between multivariate signs and ranks and zonoids and lift-zonoids
Cluster analysis, discriminant analysis and classification
Algorithms and software, R packages
Biometrical and signal processing applications

Researchers

Hannu Oja , Professor, leader of the group
Jaakko Nevalainen , Professor (University of Turku), Jyrki Möttönen (university of Helsinki), Esa Ollila (University of Oulu), Sara Taskinen (University of Jyväskylä)
Seija Sirkiä , Jarkko Isotalo, Klaus Nordhausen , Martin Schindler, post doc researchers
Riina Haataja, Pauliina Ilmonen, Vesa Saaristo, Kari Tokola, Maarit Laaksonen, Daniel Fischer, Eero Liski, Sylvia Kiwuwa, doctoral students

Doctoral Theses

Ahti Niinimaa (1992, University of Oulu); Jyrki Möttönen (1997, University of Oulu); Samuli Visuri (2001, Helsinki Technical University); Esa Ollila (2002, University of Jyväskylä); Sara Taskinen (2003, University of Jyväskylä); Jaakko Nevalainen (2007; University of Tampere); Seija Sirkiä (2007, University of Jyväskylä); Klaus Nordhausen (2008, University of Tampere)

Cooperation

The research group was a member in the ESF Network "Statistical Analysis of Complex Data with Robust and Related Statistical Methods (SACD)" running from Jan 1 2004 to Dec 31 2006.
The research is conducted in a close cooperation with Statistical Signal Processing Research Group , Helsinki Technical University, leader professor Visa Koivunen .
Part of the research has been conducted conducted in cooperation with other groups in the Laboratory of Data Analysis, leader Professor Pasi Koikkalainen, and the CMCM institute , University of Jyväskylä, leader Professor Antti Penttinen.
Recruiting and education of students: The Finnish Graduate School in Stochastics and Statistics (FGSS) , Tampere Graduate School in Information Science and Engineering (TISE) , Jyväskylä Graduate School in Computing and Mathematical Sciences (COMAS) .
This research is partly done in co-operation with world class scientists from United States ( Tom Hettmansperger , Somnath Datta , Ron Randles , Robert Serfling , David Tyler ) , Belgium ( Christophe Croux , Marc Hallin , Davy Paindaveine ), Canada ( Denis Larocque ) Russia (Gleb Koshevoy, Yuri Tyurin) and Switzerland (Jürg Hüsler).

Funding

In 2001-2003, the work of the research group has been supported by a research grant from Academy of Finland ('Nonparametric and robust multivariate methods in data analysis and signal processing', a consortium formed by our research group and a group at Signal Processing Laboratory, HUT, leader Professor Visa Koivunen).
In 2004-2006, the work of the research group was supported by a research grant from Academy of Finland ('Nonparametric and robust multivariate methods').
In 2007-2009, the work of the research group is supported by a new research grant from Academy of Finland ('Nonparametric and robust multivariate methods').
In 2008-2012, PI Hannu Oja works as an academy professor.