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Switching nonparametric regression models

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  • Camila P. E. de Souza
  • Nancy E. Heckman

Abstract

We propose a methodology to analyse data arising from a curve that, over its domain, switches among J states. We consider a sequence of response variables, where each response y depends on a covariate x according to an unobserved state z . The states form a stochastic process and their possible values are j =1, ... , J . If z equals j the expected response of y is one of J unknown smooth functions evaluated at x . We call this model a switching nonparametric regression model. We develop an Expectation-Maximisation algorithm to estimate the parameters of the latent state process and the functions corresponding to the J states. We also obtain standard errors for the parameter estimates of the state process. We conduct simulation studies to analyse the frequentist properties of our estimates. We also apply the proposed methodology to the well-known motorcycle dataset treating the data as coming from more than one simulated accident run with unobserved run labels.

Suggested Citation

  • Camila P. E. de Souza & Nancy E. Heckman, 2014. "Switching nonparametric regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 617-637, December.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:617-637
    DOI: 10.1080/10485252.2014.941364
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    References listed on IDEAS

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    1. Hardle, W. & Marron, J. S., 1995. "Fast and simple scatterplot smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 1-17, July.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
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    Cited by:

    1. Adam, Timo & Mayr, Andreas & Kneib, Thomas, 2022. "Gradient boosting in Markov-switching generalized additive models for location, scale, and shape," Econometrics and Statistics, Elsevier, vol. 22(C), pages 3-16.
    2. Michels, Rouven & Ötting, Marius & Langrock, Roland, 2023. "Bettors’ reaction to match dynamics: Evidence from in-game betting," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1118-1127.

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