Spline Estimator in Multi-Response Nonparametric Regression Model

  • Budi Lestari Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Jember
  • Nyoman Budiantara Department of Statistics, Faculty of Mathematics and Natural Sciences, Sepuluh Nopember Institute of Technology
  • Sony Sunaryo Department of Statistics, Faculty of Mathematics and Natural Sciences, Sepuluh Nopember Institute of Technology
  • Muhammad Mashuri Department of Statistics, Faculty of Mathematics and Natural Sciences, Sepuluh Nopember Institute of Technology

Abstract

In many applications two or more dependent variables are observed at several values of the independent variables, such as at time points. The statistical problems are to estimate functions that model their dependences on the independent variables, and to investigate relationships between these functions. Nonparametric regression model, especially smoothing splines provides powerful tools to model the functions which draw association of these variables. Penalized weighted least-squares is used to jointly estimate nonparametric functions from contemporaneously correlated data. In this paper we formulate the multi-response nonparametric regression model and give a theoretical method for both obtaining distribution of the response and estimating the nonparametric function in the model. We also estimate the smoothing parameters, the weighting parameters and the correlation parameter simultaneously by applying three methods: generalized maximum likelihood (GML), generalized cross validation (GCV) and leaving-out-one-pair cross validation (CV).

 

Published
2010-01-03
How to Cite
LESTARI, Budi et al. Spline Estimator in Multi-Response Nonparametric Regression Model. Jurnal ILMU DASAR, [S.l.], v. 11, n. 1, p. 17-22, jan. 2010. ISSN 2442-5613. Available at: <https://jurnal.unej.ac.id/index.php/JID/article/view/102>. Date accessed: 29 mar. 2024.
Section
General

Keywords

Multi-response Nonparametric Regression Model; Penalized Weighted Least-Squares; Generalized Maximum Likelihood; Generalized Cross Validation; leaving-out-one-pair cross validation