Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression

International Conference on Mathematics: Education, Theory and Application

数学;教育

Afifah, Ngizatul^1 ; Budiantara, I. Nyoman^1 ; Latra, I. Nyoman^1

Statistics Departement, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia^1

关键词: Generalized cross validation;    Penalized least-squares;    Regression curve;    Semi-parametric regressions;    Semiparametric regression model;    Smoothing parameter;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/855/1/012002/pdf
DOI  :  10.1088/1742-6596/855/1/012002

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

Given paired observation (xi, v1i, v2i, , vpi, t1i, t2i, , tqi, yi), i = 1, 2, , n, follow the additive semiparametric regression model yi= μ(xi, vi, ti) +i, where μ(xi,vt,ti)=f(xi)+∑j=1pgj(νji)+∑s=1qhs(tsi) vi= (v1i, v2i, , vpi)′, and ti= (t1i, t2i, , tqi)′. Random errorsiis a normal distribution with mean 0 and variance σ2. To obtain a mixed estimator μ(xi, vi, ti), the regression curve f(xi) is approached by linier parametric, gj(vji) is kernel with bandwidths Φ = (φ1, φ2, , φp)′and the regression curve component fourier series hs(tsi) is approached by with oscillation paremeter N. The estimator is where . Penalized Least Squares (PLS) method give Minc,β{ L(c)+L(β)+∑s=1qθsS(Hs(tsi)) } with smoothing parameter θ = (θ1, θ2, , θq)′, the estimator f(x) is and is , where and . So that, μΦ,θ,N(vi,ti)=Z(Φ,θ,N)y is the mixed estimator of μ(vi, ti) where Z(Φ, θ, N) = C(Φ, θ, N) + V(Φ) + E(Φ, θ, N) Matrix C(Φ, θ, N), V(Φ) and E(Φ, θ, N) are depended on Φ, θ and N. Optimal Φ, θ and N can be obtained by the smallest Generalized Cross Validation (GCV).