Smooth residual bootstrap for empirical processes of non-parametric regression residuals

Scandinavian Journal of Statistics

Volumn 36, Issue 2, 2009, Pages 204-228

  Neumeyer, Natalie ^a  

^a UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Empirical distribution function; Goodness of fit tests; Kernel estimators; Resampling

Indexed keywords

EID: 67949109563     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2008.00628.x     Document Type: Article

References (40)

1. Akritas, M. & Van Keilegom, I. (2001). Non-parametric estimation, of the residual distribution. Scand. J. Statist. 28, 549-567.
2. Bai, J. (1994). Weak convergence of the sequential empirical processes of residuals in ARMA models. Ann. Statist. 22, 2051-2061.
3. Beran, R. J., Le Cam, L. & Millar, P. W. (1987). Convergence of stochastic empirical, measures. J. Multivariate Anal. 23, 159-168.
4. Boldin, M. V. (1982). Estimation of the distribution of noise in an autoregression scheme. Theory Probab. Appl. 27, 866-871.
5. Cheng, F. (2002). Consistency of error density and. distribution function estimation in nonparametric regression. Statist. Probab. Lett., 59, 257-270.
6. Cheng, F. (2004). Weak and strong uniform consistency of a kernel error density estimator in nonparametric regression. J. Statist. Plann. Inference 119, 95-107.
7. 1 regression. J. Amer. Statist. Assoc. 88, 1310-1316.
8. Delgado, M. A. & González-Manteiga, W. (2001). Significance testing in nonparametric regression based on the bootstrap. Ann. Statist. 29, 1469-1507.
9. Dette, H., Neumeyer, N. & Van Keilegom, I. (2007). A new test for the parametric form, of the variance function in nonparametric regression. J. Roy. Statist, Soc., Ser. B Statist. Methodol 69, 903-917.
10. Durbin, J. (1973). Weak convergence of the sample distribution function when parameters are estimated. Ann. Statist. 1, 279-290.
11. Härdie, W. & Bowman, A. W. (1988). Bootstrapping in nonparametric regression: local adaptive smoothing and confidence bands. J. Amer. Statist. Assoc. 83, 102-1.10.
12. Härdie, W. & Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. Ann. Statist. 21, 1926-1947.
13. Karunamuni, R. J. & Zhang, S. (2007). Some improvement on a boundary corrected kernel density estimator. Statist. Probab. Lett. 78, 499-507.
14. Koul, H. L. (1970). Some convergence theorems for ranks and weighted empirical cumulatives. Ann. Math. Statist. 41, 1768-1773.
15. Koul, H. L. (2002). Weighted empirical processes in dynamic nonlinear models, 2nd edn. Springer, New York.
16. Koul, H. L. & Lahiri, S. N. (1994). On bootstrapping M-estimated residual processes in multiple linear regression models. J. Multivariate Anal. 49, 255-265.
17. Koul, H. L. & Levental, S. (1.989). Weak convergence of the residual empirical process in explosive autoregression. Ann. Statist. 17, 1784-1794.
18. Loynes, R. M. (1.980). The empirical distribution function of residuals from generalized regression. Ann. Statist. 8, 285-298.
19. Mammen, E. (1.996). Empirical process of residuals for high-dimensional linear models. Ann., Statist. 24, 307-335.
20. Mora, J. & Neumeyer, N. (2005). The two-sample problem with regression errors: an empirical process approach. Preprint, http://www.math.uni- hamburg.de/home/neumeyer/paperjm.pdf
21. Müller, H.-G. (1.984). Boundary effects in nonparametric curve estimation. Compstat 1.984. Physica Verlag, Heidelberg, 84-89.
22. Müller, U, Schick, A. & Wefelmeyer, W. (2007). Estimating the error distribution function, in semiparametric regression. Statist. Decisions. 25, 1-1.8.
23. Neumeyer, N. (2006). Bootstrap procedures for empirical processes of nonparametric residuals. Habilitationsschrift, Ruhr-Universität Bochum. http://www.math.uni-hamburg.de/home/neumeyer/habil.ps
24. Neumeyer, N. (2008). A bootstrap version of the residual-based smooth empirical distribution function. J. Nonparametr. Statist, 20, 153-174.
25. Neumeyer, N. & Dette, H. (2005). A. note on one-sided nonparametric analysis of covariance by ranking residuals. Math. Methods Statist. 14, 80-104.
26. Neumeyer, N. & Van Keilegom, I. (2008). Estimating the error distribution in nonparametric multiple regression with applications to model, testing. Preprint, http://www.math.uni-h.am.burg.de/ research/ims.html
27. Pardo-Fernández, X C. (2007). Comparison of error distributions in nonparametric regression. Statist. Probab. Lett. 77, 350-356.
28. Pardo-Fernández, J. C., Van Keilegom, I. & González-Manteiga, W (2007). Testing for the equality of k regression curves. Statist. Sinica 17, 1115-1137.
29. Pollard, D. (1984). Convergence of stochastic processes. Springer, New York.
30. Portnoy, S. (1.986). Asymptotic behavior of the empiric distribution of M-estimated residuals from a regression model with many parameters. Ann. Statist. 14, 1152-1170.
31. Rice, J. (1984a). Bandwidth choice for nonparametric regression. Ann. Statist. 12, 1215-1230.
32. Rice, J. (1.984b). Boundary modification for kernel regression. Comm., Statist. Theory Methods 13, 893-900.
33. Ruppert, D., Sheather, S. J. & Wand, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc, 90, 1257-1270.
34. Schick, A. & Wefelmeyer, W. (2002). Estimating the innovation distribution in nonlinear autoregressive models. Ann. Inst. Statist. Math. 54, 245-260.
35. Speckman, P. L., Chiu, J.-E., Hewett, X E. & Bertelson, S. E. (2001). A one-sided test adjusting for covariates by ranking residuals following smoothing. Technical report, http://www.stat.missouri.edu/ ~speckman/pub.html
36. Stute, W. (1997). Nonparametric model checks for regression. Ann. Statist. 25, 613-641.
37. van der Vaart, A. W. (1.998). Asymptotic statistics. Cambridge University Press, Cambridge.
38. van der Vaart, A. W. & Wellner, X A. (1996). Weak convergence and empirical processes. Springer, New York.
39. Van Keilegom, I., González-Manteiga, W. & Sánchez Sellero, C. (2008). Goodness-of-fit tests in parametric regression based on the estimation of the error distribution. Test 17, 401-415.
40. Wu, C-F. J. (1.986). Jackknife, bootstrap and other resampling methods in regression analysis. Ann. Statist. 14, 1261-1350.