Chaubey, Yogendra P. and Laib, Naâmane and Sen, Arusharka (2008) *A Smooth Estimator of Regression Function for Non-Negative Dependent Random Variables.* Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.

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## Abstract

Commonly used kernel regression estimators may not provide admissible values of the regression function or its functionals at the boundaries, for regressions with restricted support. Any smoothing method will become less accurate near the boundary of the observation interval because fewer observations can be averaged, and thus variance or bias can be affected. Here, we adapt Chaubey et al. (2007)'s method of density estimation for nonnegative random variables to define a smooth estimator of the regression function. The estimator is based on a generalization of Hille's lemma and a perturbation idea. Its uniform consistency and asymptotic normality are obtained, for the sake of generality, under a stationary ergodic process assumption for the data . The asymptotic mean squared error is derived and the optimal value of

smoothing parameter is also discussed. Graphical illustration of the proposed estimator are provided on

simulated as well as real-life data.

Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
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Item Type: | Monograph (Technical Report) |

Authors: | Chaubey, Yogendra P. and Laib, Naâmane and Sen, Arusharka |

Series Name: | Department of Mathematics & Statistics. Technical Report No. 2/08 |

Corporate Authors: | Concordia University. Department of Mathematics & Statistics |

Institution: | Concordia University |

Date: | March 2008 |

Keywords: | Ergodic processes, Hille's Lemma, gamma density function, martin-gale difference, normality, prediction, regression function |

ID Code: | 6685 |

Deposited By: | DIANE MICHAUD |

Deposited On: | 03 Jun 2010 16:09 |

Last Modified: | 08 Dec 2010 18:20 |

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