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Generalised kernel smoothing for non-negative stationary ergodic processes


Generalised kernel smoothing for non-negative stationary ergodic processes

Chaubey, Yogendra P., Laïb, Naâmane and Sen, Arusharka (2010) Generalised kernel smoothing for non-negative stationary ergodic processes. Journal of Nonparametric Statistics, 22 (8). pp. 973-997. ISSN 1048-5252

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Laib_GeneralizedRegression_Ver1_Chaub.pdf - Submitted Version

Official URL: http://dx.doi.org/10.1080/10485251003605120


In this paper, we consider a generalised kernel smoothing estimator of the regression function with nonnegative
support, using gamma probability densities as kernels, which are non-negative and have naturally varying shapes. It is based on a generalisation of Hille’s lemma and a perturbation idea that allows us to deal with the problem at the boundary. Its uniform consistency and asymptotic normality are obtained at interior and boundary points, under a stationary ergodic process assumption, without using traditional mixing conditions. The asymptotic mean squared error of the estimator is derived and the optimal value of smoothing parameter is also discussed. Graphical illustrations of the proposed estimator are provided
for simulated as well as for real data. A simulation study is also carried out to compare our method with the competing local linear method.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Authors:Chaubey, Yogendra P. and Laïb, Naâmane and Sen, Arusharka
Journal or Publication:Journal of Nonparametric Statistics
Date:29 March 2010
Digital Object Identifier (DOI):10.1080/10485251003605120
Keywords:ergodic processes; Hille’s lemma; gamma density; martingale difference; mixing; normality; prediction; regression function
ID Code:36102
Deposited On:06 Feb 2012 18:35
Last Modified:18 Jan 2018 17:36
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