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Asymptotic results in segmented multiple regression

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  • Kim, Jeankyung
  • Kim, Hyune-Ju

Abstract

This paper studies the asymptotic behavior of the least squares estimators in segmented multiple regression. For a model with more than one partitioning variable, each of which has one or more change-points, we study the asymptotic properties of the estimated change-points and regression coefficients. Using techniques in empirical process theory, we prove the consistency of the least squares estimators and also establish the asymptotic normality of the estimated regression coefficients. For the estimated change-points, we obtain their consistency at the rates of or 1/n, with or without continuity constraints, respectively. The change-points estimated under the continuity constraints are also shown to asymptotically have a multivariate normal distribution. For the case where the regression mean functions are not assumed to be continuous at the change-points, the asymptotic distribution of the estimated change-points involves a step function process, whose distribution does not follow a well-known distribution.

Suggested Citation

  • Kim, Jeankyung & Kim, Hyune-Ju, 2008. "Asymptotic results in segmented multiple regression," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2016-2038, October.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:9:p:2016-2038
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    References listed on IDEAS

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    1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. Yu, Binbing & Barrett, Michael J. & Kim, Hyune-Ju & Feuer, Eric J., 2007. "Estimating joinpoints in continuous time scale for multiple change-point models," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2420-2427, February.
    4. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
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    Cited by:

    1. Chih‐Hao Chang & Kam‐Fai Wong & Wei‐Yee Lim, 2023. "Threshold estimation for continuous three‐phase polynomial regression models with constant mean in the middle regime," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 4-47, February.
    2. Beran, Jan & Weiershäuser, Arno, 2011. "On spline regression under Gaussian subordination with long memory," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 315-335, February.
    3. Gabriela Ciuperca, 2014. "Model selection by LASSO methods in a change-point model," Statistical Papers, Springer, vol. 55(2), pages 349-374, May.

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