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Change Point Estimation in Regression Models with Fixed Design

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Mathematical and Statistical Models and Methods in Reliability

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

In this paper, we consider a simple regression model with change points in the regression function which can be one of two types: A so called smooth bent-line change point or a discontinuity point of a regression function. In both cases we investigate the consistency of the M-estimates of the change points. It turns out that the rates of convergence are n 1 ∕ 2 or n, respectively, where n denotes the sample size in a fixed design. In addition, the asymptotic distributions of the change point estimators are investigated.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, Stuttgart, Germany

    Maik Döring & Uwe Jensen

Authors
  1. Maik Döring
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  2. Uwe Jensen
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Corresponding author

Correspondence to Uwe Jensen .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, Gubkin Russian State University of Oil a, Leninskii Prospekt 65, Moskva, 117917, Russian Federation

    V.V. Rykov

  2. McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, L8S 4K1, Ontario, Canada

    N. Balakrishnan

  3. Université Victor Segalen Bordeaux 2, I’lnstitut de Mathématiques de Bordeaux, Bordeaux Cedex, 33076, France

    M.S. Nikulin

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Döring, M., Jensen, U. (2010). Change Point Estimation in Regression Models with Fixed Design. In: Rykov, V., Balakrishnan, N., Nikulin, M. (eds) Mathematical and Statistical Models and Methods in Reliability. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4971-5_15

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