PERBANDINGAN ESTIMATOR REGRESI NONPARAMETRIK MENGGUNAKAN METODE FOURIER DAN METODE WAVELET

Abstract



Let  be independent observation data and follows a model  Y_i = f(X_i) + e_I ,

 i =1,2,...,n  with f is an unknown regression function and e_i 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.