PEMILIHAN THRESHOLD OPTIMAL PADA ESTIMATOR REGRESI WAVELET THRESHOLDING DENGAN METODE CROSS VALIDASI

Abstract

If x is a predictor variable and y is a response  variable of  the regression model y = f (x)+ Î with  f is a regression function which not yet been known and Î is independent random variable with mean 0 and variance , hence function f can be estimated by parametric and nonparametric approach. In this paper function f is estimated with a nonparametric approach. Nonparametric approach that used is a wavelet shrinkage or a wavelet threshold method. In the function estimation with a wavelet threshold method,  the value of  threshold has  the most important role to determine  level of smoothing estimator. The small threshold give function estimation very no smoothly, while  the big value of threshold give function estimation very smoothly. Therefore the optimal value of threshold should be selected to determine the optimal function estimation. One of the methods to determine the optimal value of threshold by minimize a cross validation function. The cross validation method that be used is two-fold cross validatiaon. In this cross validation, it compute the predicted value by using a half of data set. The original data set is split  into two subsets of equal size : one containing only the even indexed data, and the other, the odd indexed data. The odd data will be used to predict the even data, and vice versa. Based on  the result of data analysis, the optimal threshold with cross validation method is not uniq, but they give the  uniq of wavelet thersholding regression estimation.

Keywords : Nonparametric Regression, Wavelet Threshold Estimator, Cross Validation.