PERBANDINGAN ESTIMATOR REGRESI NONPARAMETRIK MENGGUNAKAN METODE FOURIER DAN METODE WAVELET

Abstract

Let be independent observation data and follows a model Yi = f(Xi) + I , i =1,2,...,n with f is an unknown regression function and i are independent random variables with mean 0 and variance 2. 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.