Specification tests for the distribution of errors in nonparametric regression: A martingale approach

Journal of Nonparametric Statistics

Volumn 21, Issue 4, 2009, Pages 441-452

  Mora, Juan ^a   Pérez Alonso, Alicia ^b  

^a UNIVERSITY OF ALICANTE   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Empirical processes; Nonparametric regression; Specification tests

Indexed keywords

EID: 70449436403     PISSN: 10485252     EISSN: 10290311     Source Type: Journal    
DOI: 10.1080/10485250802666192     Document Type: Article

References (22)

1. J. Durbin, Weak convergence of the sample distribution function when parameters are estimated, Ann. Statist. 1 (1973), pp. 279-290.
2. M.Akritas and I.Van Keilegom, Non-parametric estimation of the residual distribution, Scand. J. Statist. 28 (2001) pp. 549-567.
3. V.E. Khmaladze, Goodnessoffitproblemandscanninginnovationsmartingales, Ann.Statist.21(1993),pp.798-829.
4. Y.P. Mack and B.W. Silverman, Weak and strong uniform consistency of kernel regression estimates, Z. Wahrsch. verw. Gebiete 61 (1982), pp. 405-415.
5. W. Härdle and E. Mammen, Comparing nonparametric versus parametric regression fits, Ann. Statist. 21 (1993), pp. 1926-1947.
6. N. Neumeyer, H. Dette, and E.R. Nagel, Bootstrap tests for the error distribution in linear and nonparametric regression models, Aust. N. Z. J. Statist. 48 (2006), pp. 129-156.
7. U.U. Müller, A. Schick, and W. Wefelmeyer, Estimating the error distribution function in semiparametric regression, Statist. Decis. 25 (2007), pp. 1-18.
8. J. Bai, Testingparametricconditionaldistributionsofdynamicmodels, Rev.Econom.Statist.85(2003),pp.531-549.
9. H.L. Koul and L. Sakhanenko, Goodness-of-fit testing in regression: A finite sample comparison of bootstrap methodology and Khmaladze transformation, Statist. Probab. Lett. 74 (2005), pp. 290-302.
10. J. Mora and N. Neumeyer, The two-sample problem with regression errors: An empirical process approach, IVIE Working Paper AD 18 (2005). Available at http://www.ivie.es/downloads/docs/wpasad/wpasad-2005-18.pdf.
11. A. Tsigroshvili, Some notes on goodness-of-fit and innovations martingales, Proc. A. Razmadze Math. Inst. 117 (1998), pp. 89-102.
12. V.K. Rohatgi and A.K.M.E. Saleh, An Introduction to Probability and Statistics, 2nd ed., Wiley-Interscience, New York, 2001.
13. G. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics, Wiley, NewYork, 1986.
14. E.D. Rothman and M. Woodroofe, A Cramér-von Mises type statistic for testing symmetry, Ann. Math. Statist. 43 (1972), pp. 2035-2038.
15. C. Fernández and M.F.J. Steel, On Bayesian modeling of fat tails and skewness, J. Am. Statist. Assoc. 93 (1998), pp. 359-371.
16. T. Kloek and H. van Dijk, Efficient estimation of income distribution parameters, J. Econom. 8 (1978), pp. 61-74.
17. J.B. McDonald and R.J. Butler, Regressionmodelsforpositiverandomvariables, J.Econom.43(1990),pp.227-251.
18. H. Dette, N. Neumeyer, and S. Kusi-Appiah, Testing symmetry in nonparametric regression models, J. Nonparametr. Statist. 14 (2002), pp. 477-494.
19. N. Neumeyer and H. Dette, Testing for symmetric error distribution in nonparametric regression models, Statist. Sin. 17 (2007), pp. 775-795.
20. J. Franke, J.P. Kreiss, and E. Mammen, Bootstrap of kernel smoothing in nonlinear time series, Bernoulli 8 (2002), pp. 1-37.
21. B.E. Hansen, Uniform convergence rates for kernel estimation with dependent data, Econometric Theory 24 (2008), pp. 726-748.
22. A.W. van der Vaart and J.A. Wellner, Weak Convergence and Empirical Processes, Springer-Verlag, NewYork, 1996