SONGKLANAKARIN JOURNAL OF SCIENCE & TECHNOLOGY

Volume 42, No. 03, Month MAY, Year 2020, Pages 533 - 548

Spline estimator and its asymptotic properties in multiresponse nonparametric regression model

Budi Lestari, Fatmawati, I Nyoman Budiantara

Abstract Download PDF

In applications, we often meet the problem where more than one response variable is observed at several values of predictor variables, and these responses are correlated with each other. The multiresponse nonparametric regression model approach is appropriate to model the functions which represent relationship between response and predictor variables. This relationship is drawn by the regression function. The principal problem of this model approach is estimating of the regression function of this model. The spline estimator is one of the most popular estimators used for estimating it. In this paper we discuss methods to obtain a smoothing spline estimator for estimating the regression function, to get a covariance matrix estimator, and to choose an optimum smoothing parameter. In addition, we investigate the asymptotic properties of the smoothing spline estimator.

Keywords

multiresponse nonparametric regression, covariance matrix, spline estimator, smoothing parameter, asymptotic properties

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