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Estimation of a semiparametric mixture of regressions model

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  • Pierre Vandekerkhove

Abstract

We introduce in this paper a new mixture of regressions model which is a generalisation of the semiparametric two-component mixture model studied in Bordes, Delmas, and Vandekerkhove [(2006b), 'Semiparametric Estimation of a Two-component Mixture Model When a Component is Known', Scandinavian Journal of Statistics , 33, 733-752]. Namely, we consider a two-component mixture of regressions model in which one component is entirely known while the proportion, the slope, the intercept, and the error distribution of the other component are unknown. Our model is said to be semiparametric in the sense that the probability density function (pdf) of the error involved in the unknown regression model cannot be modelled adequately by using a parametric density family. When the pdfs of the errors involved in each regression model are supposed to be zero-symmetric, we propose an estimator of the various (Euclidean and functional) parameters of the model, and establish under mild conditions their almost sure rates of convergence. Finally, the implementation and numerical performances of our method are discussed using several simulated data sets and one real high-density array data set (ChIP-mix model).

Suggested Citation

  • Pierre Vandekerkhove, 2013. "Estimation of a semiparametric mixture of regressions model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 181-208, March.
  • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:181-208
    DOI: 10.1080/10485252.2012.741236
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    Cited by:

    1. Yuzhu Tian & Manlai Tang & Maozai Tian, 2016. "A class of finite mixture of quantile regressions with its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1240-1252, July.
    2. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    3. Xiaotian Zhu & David R. Hunter, 2019. "Clustering via finite nonparametric ICA mixture models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 65-87, March.
    4. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, March.

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