Perbandingan regresi parametrik dan regresi nonparametric=Comparing Parametric Versus nonparametric Regression Fits

Given n iid observation i(X,,Y):i=1,2,...,n) with unknown re ssion function m(.) = E(Y,/X,=.). It also can be written as Y, = m(Xi) + ei with E(Ei/X,) = 0. The are not assumed to be conditionally iid. Regression function m(.) can be estimated by parametric and nonparametric methods. In general, there will be visible differences between parametric and nonparametric curve estimation. It is therefore quite natural to compare these in order to decide whether j the parametric model could be justified. Given Illy(. ) a parametric estimator of m(.). Let tilh( . ) the Nadaraya-Watson\u27s nonparametric estimator of m(.). The statistic = nh1/2j (rilh(x) â K ne(x) )21t(x)dx with Kh,n is a smoothing operator and it is wheighted function, can be used to test approprietness of parametric model. The critical value is determinated by asymtotic distribution of T. The naive bootstrap approach does not work and as alternative the wild bootstrap does. Key words : parametric regression, nonparametric regression, bootstrap