On the Goodness-of-fit Test in Regression Using the Difference Between Nonparametric and Parametric Fits

  • Hong, Chang-Kon (Department of Statistics, Pusan National University) ;
  • Joo, Jae-Seon (Department of Statistics, Pusan National University)
  • Published : 2001.04.01

Abstract

This paper discusses choosing the weight function of the Hardle and Mammen statistic in nonparametric goodness-of-fit test for regression curve. For this purpose, we modify the Hardle and Mammen statistic and derive its asymptotic distribution. Some results on the test statistic from the wild bootstrapped sample are also obtained. Through Monte Carlo experiment, we check the validity of these results. Finally, we study the powers of the test and compare with those of the Hardle and Mammen test through the simulation.

Keywords

References

  1. The Annals of Statistics v.14 Comment on Jackknife, bootstrap and other resampling methods in regression analysis Beran,R.;C.F.J.Wu
  2. The Annals of Statistics v.12 Detecting a smooth signal : Optimality of cusum based procedures Buckley,M.J.
  3. The Annals of Statistics v.16 Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models Cox,D.;Koh,E.Washable;Yandell,B.
  4. Probability Theory Related Fields v.75 A central limit theorem for generalized quadratic forms De Jong
  5. The Annals of Statistics v.20 Testing goodness-of-fit in regression via order selection criteria Eubank,R.L.;Hart,J.D.
  6. The Annals of Statistics v.16 Asymptotic comparison of Cramer-von Mises and nonparametric function estimation techniques for testing goodness-of-fit Eubank,R.L.;LaRiccia,V.N.
  7. Journal of the American Statistical Association v.85 Testing the goodness-of-fit of linear models via nonparametric regression techniques Eubank,R.L.;Spiegelman,C.
  8. Applied Nonparametric Regression Econometric Society Monograph Series 19 Hardle,W.
  9. The Annals of Statistics v.21 Comparing nonparametric versus parametric regression fits Hardle,W.;Mammen,E.
  10. Journal of the American Statistical Association v.83 How far are automatically chosen regression smoothing parameters from their optimal? Hardle,W.;Marron,J.S.
  11. The Annals of Statistics v.16 Bootstrap procedures under some non i.i.d. models Liu,R.
  12. Lecture notes in statist v.77 When does bootstrap work : Asymptotic Results and Simulations Mammen,E.
  13. The Annals of Statistics v.21 Bootstrap and wild bootstrap for high dimensional linear models Mammen,E.
  14. Biometrika v.76 A cubic spline extension of the Durbin-Watson test Munson,P.J.;Jernigan,R.W.
  15. Technometrics v.29 The use of marginal likelihood for a diagnostic test for the goodness of fit of the simple linear regression model Yanagimoto,T.;Yanagimoto,M.
  16. The Annals of Statistics v.29 Jackknife, bootstrap and other resampling methods in regression analysis(with discussion) Wu,C.F.J.