PERBANDINGAN ESTIMATOR REGRESI NONPARAMETRIK MENGGUNAKAN METODE FOURIER DAN METODE WAVELET

Suparti Suparti



Abstract




Let  be independent observation data and follows a model  Yi = f(Xi) + eI ,

 i =1,2,...,n  with f is an unknown regression function and ei are independent random variables with mean 0 and variance s2. The function f could be estimated by parametric and nonparametric appro-aches. In nonparametric approach, the function f is assumed to be a smooth function or quadratic integrable function. If f belongs to the Hilbert space L2(R) then the function f could be estimated by estimator of orthogonal series, especially by Fourier series estimator. Another estimator of orthogonal series  which could be use  to estimate f is wavelet estimator. Wavelet estimator is an extention of Fourier series estimator  but it is more effective than the Fourier series estimator because the its IMSE converges to zero quicker than the Fourier series estimator.


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Jurnal Matematika, Fakultas Sains dan Matematika, Universitas Diponegoro. Jl. Prof. Sudarto Tembalang. telp/fax (024)76480922 Semarang 50275