### I Nyoman Budiantara, Dedy Dwi Prastyo : *Mixture model of spline truncated and kernel in multivariable nonparametric regression*

Prof. Dr. Drs. I Nyoman Budiantara M.Si

Dedy Dwi Prastyo S.Si., M.Si.

2nd International Conference on Mathematical Sciences and Statistics (ICMSS)

Abstract

Given the data (x_{1i}, x_{2i},…, x_{pi}, t_{1i}, t_{2i},…, t_{qi}, y_i) with predictors (x_{si}, t_{ki}) and response variables y_i are assumed to follow unknown function such that their dependence can be approximated by a nonparametric regression model \tilde{y} = \tilde{µ}(x,t) + \tilde{e} = \sum_{i=1}^{p} \tilde{f}s(x) + \sum_{k=1}^{q} \tilde{g} k(t) + \tilde{e}. The component \tilde{f}s(x) is approximated by additive spline regression with p-number of predictors whereas \tilde{g}(t) is approximated by kernel regression with q-number of predictors. The error \tilde{e} is assumed normally distributed with mean zero and constant variance. The objective of this article is to provide the estimators of \tilde{f}s(x)f˜^s(x) and \tilde{g}k(t) as well as the mixture model \tilde{µ}(x,t) by means of Maximum Likelihood Estimation (MLE) method.