Convergence analysis of central and minimax algorithms in scalar regressor models

Akcay H., At N.

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, vol.18, no.1, pp.66-99, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1007/s00498-005-0162-7
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.66-99
  • Keywords: system identification, membership-set, central algorithm, minimax algorithm, Chebyshev center, parameter estimate variance, convergence analysis, WORST-CASE IDENTIFICATION, FINITE-SAMPLE PROPERTIES, ROBUST IDENTIFICATION, MEMBERSHIP-SET, COMPLEXITY, OPTIMIZATION, SIZE
  • Anadolu University Affiliated: No


In this paper, the estimation of a scalar parameter is considered with given lower and upper bounds of the scalar regressor. We derive non-asymptotic, lower and upper bounds on the convergence rates of the parameter estimate variances of the central and the minimax algorithms for noise probability density functions characterized by a thin tail distribution. This presents an extension of the previous work for constant scalar regressors to arbitrary scalar regressors with magnitude constraints. We expect our results to stimulate further research interests in the statistical analysis of these set-based estimators when the unknown parameter is multi-dimensional and the probability distribution function of the noise is more general than the present setup.