Publish In |
International Journal of Management and Applied Science (IJMAS)-IJMAS |
Journal Home Volume Issue |
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Issue |
Volume-3,Issue-2 ( Feb, 2017 ) | |||||||||
Paper Title |
Mixed Estimator of Kernel and Fourier Series in Nonparametric Regression | |||||||||
Author Name |
Ngizatul Afifah, I Nyoman Budiantara, I Nyoman Latra | |||||||||
Affilition |
Master’s Program Student of Statistics Departement, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Lecturer of Statistics Departement, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia | |||||||||
Pages |
71-76 | |||||||||
Abstract |
Lets paired the observation v 1 i , v 2 i , ..., v pi , t 1 i , t 2 i , ..., t qi , y i , i 1, 2,..., n , follow the additive nonparametric v i , t i i , where v regression model y i p , t i i q g v h t , j ji s j 1 si s 1 v i v 1 i , v 2 i ,..., v pi , and t i t 1 i , t 2 i ,..., t qi . Random errors i is a normal distribution with mean 0 and variance 2 . The aim of this study is obtain a mixed estimator v , t . In order to accomplish the aim, the regression i Φ 1 , 2 , , p and the regression curve component curve g j v ji is approached by kernel with bandwidths h s t si is fourier series where it is approached by T s t si b s t si p p The estimator g v j ji is 1 2 M a 0 s a ks cos kt si with oscillation paremeter M. k 1 p g ˆ v j j ji where j 1 j 1 i g ˆ v V Φ y . j j Based on Penalized Least Squares (PLS) ji j 1 method q Min R a a s s si s 1 q h ˆ J T t with smoothing parameter λ 1 , 2 , , q , q the estimator h t s si is s 1 q s , M t , si and s 1 h ˆ s , M t Xa ˆ λ . So that, the mixed estimator μ v , t si i i is s 1 μ ˆ Φ , λ , M v i , t i Z Φ , λ , M y where Z Φ , λ , M y V Φ S Φ , λ , M y . Matrix V Φ and S Φ , λ , M parameter Φ , smoothing parameter λ and oscillation paremeter M. Optimal Generalized Cross Validation (GCV). are depended on bandwidths Φ , λ and M can be obtained by using Keywords- Mixed Nonparametric Regression, Kernel, Fourier Series | |||||||||
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