Global dynamics of a system governing an algorithm for regression with censored and non-censored data under general errors

  • Authors:

  • Carlos Rivero;Ángela Castillo;Pedro J. Zufiria;Teófilo Valdés

  • Affiliations:

  • Departamento de Estadística e Investigación Operativa, Facultad de Ciencias Matemáticas, UCM, Madrid 28040, Spain;Departamento de Matemática Aplicada a las Tecnologias de la Información, ETSI de Telecomunicación, UPM, Madrid 28040, Spain;Departamento de Matemática Aplicada a las Tecnologias de la Información, ETSI de Telecomunicación, UPM, Madrid 28040, Spain;Departamento de Estadística e Investigación Operativa, Facultad de Ciencias Matemáticas, UCM, Madrid 28040, Spain

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2004

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Abstract

We present an investigation into the dynamics of a system, which underlies a new estimating algorithm for regression with grouped and nongrouped data. The algorithm springs from a simplification of the well-known EM algorithm, in which the expectation step of the EM is substituted by a modal step. This avoids awkward integrations when the error distribution is assumed to be general. The sequences generated by the estimating procedure proposed here define our objective system, which is piecewise linear. The study tackles the system's asymptotic stability as well as its speed of convergence to the equilibrium point. In this sense, to reduce the speed of convergence, we propose an alternative estimating procedure. Numerical examples illustrate the theoretical results, compare the proposed procedures and analyze the precision of the estimate.