Model specification tests in nonparametric stochastic regression models

Journal of Multivariate Analysis

Volumn 83, Issue 2, 2002, Pages 324-359

  Gao, Jiti ^a   Tong, Howell ^b,c   Wolff, Rodney ^d  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^d UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Additivity; Dependent process; Model determination; Nonlinear time series; Nonparametric regression; Semiparametric autoregression

Indexed keywords

EID: 0036857532     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.2001.2058     Document Type: Article

References (66)

1. G. G. Agarwal and W. J. Studden, Asymptotic integrated mean square error using least squares and bias minimizing splines, Ann. Statist. 8 (1980), 1307-1325.
2. D. W. K. Andrews, Asymptotic normality of series estimators for nonparametric and semiparametric regression models, Econometrica 59 (1991), 307-345.
3. D. Barry, Testing for additivity of a regression function, Ann. Statist. 21 (1993), 235-254.
4. G. Boente and R. Fraiman, Consistency of a nonparametric estimate of a density function for dependent variables, J. Multivariate Anal. 25 (1988), 90-99.
5. M. J. Buckley and G. K. Eagleson, An approximation to the distribution of quadratic forms in normal random variables, Austral. J. Static. A 30 (1988), 150-159.
6. C. P. Chen and P. H. Hsieh, Pointwise convergence of double trigonometric series, J. Math. Anal. Appl. 172 (1993), 582-599.
7. R. Chen and R. Tsay, Nonlinear additive ARX models, J. Amer. Statist. Assoc. 88 (1993), 955-967.
8. Chen, J. Liu, and R. Tsay, Additivity tests for nonlinear autoregression, Biometrika 82 (1995), 369-383.
9. D. D. Cox and T. Y. Kim, Moment bounds for mixing random variables useful in nonparametric function estimation, Stochastic Process. Appl. 56 (1995), 151-158.
10. P. De Jong, A central limit theorem for generalized quadratic forms, Probab. Theory Related Fields 75 (1987), 261-277.
11. R. A. DeVore and G. G. Lorentz, "Constructive Approximation," Springer-Verlag, New York, 1993.
12. P. Doukhan, "Mixing: Properties and Examples," Lecture Notes in Statistics, Vol. 85, Springer-Verlag, New York, 1995.
13. B. J. Eastwood and A. R. Gallant, Adaptive rules for seminonparametric estimators that achieve asymptotic normality, Econometric Theory 7 (1991), 307-340.
14. R. L. Eubank and J. D. Hart, Testing goodness-of-fit in regression via order selection criteria, Ann. Statist. 20 (1992), 1412-1425.
15. R. L. Eubank, J. D. Hart, D. G. Simpson, and L. A. Stefanski, Testing for additivity in nonparametric regression, Ann. Statist. 23 (1995), 1896-1920.
16. R. L. Eubank, E. L. Kambour, J. T. Kim, K. Klipple, C. S. Reese, and M. Schimek, Estimation in partially linear models, Comput. Statist. Data Anal. 29 (1998), 27-34.
17. D. E. Eumunds and V. B. Moscatelli, Fourier approximation and embeddings of Sobolev space, Dissertationes Math., 1977.
18. J. Fan, Design-adaptive nonparametric regression, J. Amer. Statist. Assoc. 87 (1992), 998-1004.
19. J. Fan and I. Gijbels, "Local Polynomial Modelling and Its Applications," Chapman & Hall, London, 1996.
20. J. Fan, W. Härdle, and E. Mammen, Direct estimation of low dimensional components in additive models, Ann. Statist. 26 (1998), 943-971.
21. J. Fan and L. S. Huang, Goodness-of-fit tests for parametric regression models, J. Amer. Statist. Assoc. 96 (2001), 640-652.
22. J. Fan and Q. W. Yao, Efficient estimation of conditional variance functions in stochastic regression, Biometrika 85 (1998), 645-660.
23. J. Fan, C. M. Zhang, and J. Zhang, Generalized likelihood ratio statistics and Wilks phenomenon, Ann. Statist. 29 (2001), 153-193.
24. Y. Fan and Q. Li, Consistent model specification tests: omitted variables and semiparametric functional forms, Econometrica 64 1996, 865-890.
25. A. R. Gallant, On the bias in flexible functional forms and an essentially unbiased form: The Fourier flexible form, J. Econometrics 15 (1981), 211-245.
26. J. Gao, Semiparametric regression smoothing of nonlinear time series, Scand. J. Statist. 25 1998, 521-539.
27. J. Gao and V. Anh, Semiparametric regression under long-range dependent errors, J. Statist. Plann. Inference 80 (1999), 37-57.
28. J. Gao and H. Liang, Asymptotic normality of pseudo-LS estimator for partially linear autoregressive models, Statist. Probab. Lett. 23 (1995), 27-34.
29. J. Gao and H. Liang, Statistical inference in single-index and partially nonlinear regression models, Ann. Inst. Statist. Math. 49 (1997), 493-517.
30. J. Gao and P. Shi, M-type smoothing splines in nonparametric and semiparametric regression models, Statist. Sinica 7 (1997), 1155-1169.
31. J. Gao, H. Tong, and R. Wolff, Adaptive orthogonal series estimation in additive stochastic regression models, Statist. Sinica 11 (2001), 1007-1027.
32. J. Gao, R. Wolff, and V. Anh, Semiparametric approximation methods in multivariate model selection, J. Complexity 17 (2001), 446-461.
33. J. Gao and T. Yee, Adaptive estimation in partially linear autoregressive models, Canad. J. Statist. 28 (2000), 571-586.
34. P. L. Gozalo and O. B. Linton, Testing additivity in generalized nonparametric regression models with estimated parameters, Private communication, 1999.
35. P. Hall, Central limit theorem for integrated square error of multivariate nonparametric density estimators, J. Multivariate Anal. 14 (1984), 1-16.
36. P. Hall, J. Kay, and D. M. Titterington, Asymptotically optimal difference based estimation of variance in nonparametric regression, Biometrika 77 (1990), 521-528.
37. W. Härdle and A. Kneip, Testing a regression model when we have smooth alternatives in mind, Scand. J. Statist. 26 (1999), 221-238.
38. W. Härdle, H. Liang, and J. Gao, "Partially Linear Models," Springer Series in Contributions to Statistics, Physica-Verlag, New York, 2000.
39. W. Härdle and E. Mannen, Comparing nonparametric versus parametric regression fits, Ann. Statist. 21 (1993), 1926-1947.
40. W. Härdle and P. Vieu, Kernel regression smoothing of time series, J. Time Ser. Anal. 13 (1992), 209-232.
41. J. Hart, "Nonparametric Smoothing and Lack-of-Fit Tests," Springer-Verlag, New York, 1997.
42. T. J. Hastie and R. J. Tibshirani, "Generalized Additive Models," Chapman & Hall, London, 1990.
43. V. Hjellvik and D. Tjøstheim, Nonparametric tests of linearity for time series, Biometrika 82 (1995), 351-368.
44. V. Hjellvik, Q. W. Yao, and D. Tjøstheim, Linearity testing using local polynomial approximation, J. Statist. Plann. Inference 68 (1998), 295-321.
45. Y. Hong and H. White, Consistent specification testing via nonparametric series regression, Econometrica 63 (1995), 1133-1159.
46. B. S. Kashin and A. A. Saakyan, "Orthogonal Series," Translations of Mathematical Monographs, Vol. 75, Amer. Math. Soc., Providence, 1989.
47. J. P. Kreiss, M. H. Neumann, and Q. W. Yao, Bootstrap tests for simple structures in nonparametric time series regression, private communication, 1999.
48. P. Lavergne and Q. H. Vuong, Nonparametric significance testing, Econometric Theory 16 (2000), 576-601.
49. Q. Li, Consistent model specification tests for time series econometric models, J. Econometrics 92 (1999), 101-147.
50. Z. D. Lu, On the geometric ergodicity of a nonlinear autoregressive model with an autoregressive conditional heteroscedastic term, Statist. Sinica 8 (1998), 1205-1217.
51. E. Masry and D. Tjøstheim, Nonparametric estimation and identification of ARCH nonlinear time series: Strong convergence and asymptotic normality, Econometric Theory 11 (1995), 258-289.
52. E. Masry and D. Tjøstheim, Additive nonlinear ARX time series and projection estimates, Econometric Theory 13 (1997), 214-252.
53. D. Nychka, S. Elliner, A. Gallant, and D. McCaffery, Finding chaos in noisy systems, J. Roy. Statist. Soc. Ser. B 54 (1992), 399-426.
54. D. Pollard, "Convergence of Stochastic Processes," Springer-Verlag, New York, 1984.
55. P. Robinson, Root-N-consistent semiparametric regression, Econometrica 56 (1988), 931-964.
56. G. Roussas and D. Ioannides, Moment inequalities for mixing sequences of random variables, Stochastic Anal. Appl. 5 (1987), 61-120.
57. P. Speckman, Kernel smoothing in partial linear models, J. Roy. Statist. Soc. Ser. B 50 (1988), 413-436.
58. C. J. Stone, Additive regression and other nonparametric models, Ann. Statist. 13 (1985), 689-705.
59. T. Teräsvirta, D. Tjøstheim, and C. W. J. Granger, Aspects of modelling nonlinear time series, in "Handbook of Econometrics" (R. F. Engle and D. L. McFadden, Eds.), Vol. 4, pp. 2919-2957, 1994.
60. D. Tjøstheim, Nonlinear time series: A selective review, Scand. J. Statist. 21 (1994), 97-130.
61. D. Tjøstheim and B. Auestad, Nonparametric identification of nonlinear time series: Projections, J. Amer. Statist. Assoc. 89 (1994a), 1398-1409.
62. D. Tjøstheim and B. Auestad, Nonparametric identification of nonlinear time series: Selecting significant lags, J. Amer. Statist. Assoc. 89 (1994b), 1410-1419.
63. H. Tong, "Nonlinear Time Series," Oxford Univ. Press, London, 1990.
64. C. M. Wong and R. Kohn, A Bayesian approach to estimating and forecasting additive nonparametric autoregressive models, J. Time Ser. Anal. 17 (1996), 203-220.
65. Q. W. Yao and H. Tong, On subset selection in nonparametric stochastic regression, Statist. Sinica 4 (1994), 51-70.
66. K. Yoshihara, Limiting behaviour of U-statistics for stationary absolutely regular process, Z. Wahrsch. Verw. Gebiete 35 (1976), 237-252.