Statistical kernel estimators for data analysis and exploration tasks: theory and applications

  • Authors:
  • Piotr Kulczycki

  • Affiliations:
  • Center for Statistical Data Analysis Methods, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland and Cracow University of Technology, Department of Automatic Control, Cracow, P ...

  • Venue:
  • MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
  • Year:
  • 2009

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Abstract

At present, statistical kernel estimators constitute the dominant -- in practice -- method of nonparametric estimation. It allows the useful characterization of probability distributions without arbitrary assumptions regarding their membership to a fixed class. In this paper their use to the basic tasks of data analysis and exploration, i.e. identification of outliers, clustering, and classification, will be considered. In every case the final result will be an algorithm ensuring that its practical implementation does not demand of the user detailed knowledge of the theoretical aspects, or laborious research and calculations. The above presented theory has been successfully applied to various practical problems of engineering and management. Two of these, the design of a fault detection and diagnosis system for automatic control purposes, and a marketing support strategy for a mobile phone operator, will be demonstrated in detail. Useful procedures for the reduction of dimensionality and size of a random sample, subordinated to the specificity of kernel estimators, will also be commented.