TY - JOUR

T1 - Spline estimator in homoscedastic multiresponse nonparametric regression model in case of unbalanced number of observations

AU - Chamidah, Nur

AU - Lestari, Budi

N1 - Publisher Copyright:
© 2016 Pushpa Publishing House, Allahabad, India.

PY - 2016/11

Y1 - 2016/11

N2 - Estimating the multi-response nonparametric regression functions which draw association of two or more dependent variables observed Keywords and phrases covariance matrix, multi-response nonparametric regression, penalized weighted least-square, reproducing kernel Hilbert space, spline estimator. at several values of the independent variables is the main problem in the multi-response nonparametric regression analysis. Multi-response nonparametric regression functions are unknown and assumed to be smooth which are contained in Sobolev space. Spline estimator can be used to estimate the nonparametric regression function by carrying out the penalized weighted least-squares optimization. In this paper, we consider homoscedastic multi-response nonparametric regression model in case of unbalanced number of observations, and give a mathematical statistics method for obtaining the spline estimator. The results show that the reproducing kernel Hilbert space approach gives solution of penalized weighted least-squares optimization for estimating homoscedastic multi-response nonparametric regression function providing the weighted spline estimator.

AB - Estimating the multi-response nonparametric regression functions which draw association of two or more dependent variables observed Keywords and phrases covariance matrix, multi-response nonparametric regression, penalized weighted least-square, reproducing kernel Hilbert space, spline estimator. at several values of the independent variables is the main problem in the multi-response nonparametric regression analysis. Multi-response nonparametric regression functions are unknown and assumed to be smooth which are contained in Sobolev space. Spline estimator can be used to estimate the nonparametric regression function by carrying out the penalized weighted least-squares optimization. In this paper, we consider homoscedastic multi-response nonparametric regression model in case of unbalanced number of observations, and give a mathematical statistics method for obtaining the spline estimator. The results show that the reproducing kernel Hilbert space approach gives solution of penalized weighted least-squares optimization for estimating homoscedastic multi-response nonparametric regression function providing the weighted spline estimator.

KW - Covariance matrix

KW - Multi-response nonparametric regression

KW - Penalized weighted least-square

KW - Reproducing kernel Hilbert space

KW - Spline estimator

UR - http://www.scopus.com/inward/record.url?scp=84994509065&partnerID=8YFLogxK

U2 - 10.17654/MS100091433

DO - 10.17654/MS100091433

M3 - Article

AN - SCOPUS:84994509065

SN - 0972-0871

VL - 100

SP - 1433

EP - 1453

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

IS - 9

ER -