Unified approach to testing functional hypotheses in semiparametric contexts

Journal of Econometrics

Volumn 127, Issue 2, 2005, Pages 225-252

  Hall, Peter ^a   Yatchew, Adonis ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Bootstrap; Convexity; Curve estimation; Density estimation; Independence; Index model; Monotonicity; Nonparametric; Parametric; Partial linear model; Positivity; Radial symmetry; Regression; Separability; Smoothing

Indexed keywords

MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; STATISTICAL TESTS; THEOREM PROVING; TIME SERIES ANALYSIS;

BOOTSTRAP; CONVEXITY; CURVE ESTIMATION; DENSITY ESTIMATION; INDEX MODELS; MONOTONICITY; PARTIAL LINEAR MODELS; RADIAL SYMMETRY; SEPARABILITY; SMOOTHING;

REGRESSION ANALYSIS;

EID: 19744364015     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2004.08.005     Document Type: Article

References (70)

1. A. Abadie Bootstrap tests for distributional treatment effects in instrumental variable models Journal of the American Statistical Association 97 2002 284 292
2. N.H. Anderson, P. Hall, and D.M. Titterington Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates Journal of Multivariate Analysis 50 1998 41 54
3. A. Azzalini, and A. Bowman On the use of nonparametric regression for checking linear relationships Journal of the Royal Statistical Society Series B 55 1993 549 557
4. B.H. Baltagi, J. Hidalgo, and Q. Li A nonparametric test for poolability using panel data Journal of Econometrics 75 1996 345 367
5. G.F. Barrett, and S.G. Donald Consistent tests for stochastic dominance Econometrica 71 2003 71 104
6. D. Barry Testing for additivity of a regression function Annals of Statistics 21 1993 235 254
7. H. Bierens Consistent model specification tests Journal of Econometrics 20 1982 105 134
8. H. Bierens A consistent conditional moment test of functional form Econometrica 58 1990 1443 1458
9. H. Bierens, and W. Ploeberger Asymptotic theory of integrated conditional moments Econometrica 65 1997 1129 1151
10. A.W. Bowman, M.C. Jones, and I. Gijbels Testing monotonicity of regression Journal of Computational and Graphical Statistics 7 1998 489 500
11. Delecroix, M., Hall, P., Vial, C., 2002. Tests for single index models that are powerful against local alternatives. Manuscript.
12. H. Dette A consistent test for the functional form of a regression based on a difference of variance estimators Annals of Statistics 27 1999 1012 1040
13. G. Ellison, and S. Ellison A simple framework for nonparametric specification testing Journal of Econometrics 96 2000 1 23
14. R. Eubank, and J. Hart Testing goodness-of-fit in regression via order selection criteria Annals of Statistics 20 1992 1412 1425
15. R. Eubank, and C. Spiegelman Testing the goodness of fit of a linear model via nonparametric regression techniques Journal of the American Statistical Association 85 1990 387 392
16. R. Eubank, J. Hart, D. Simpson, and L. Stefanski Testing for additivity in nonparametric regression Annals of Statistics 23 1995 1896 1920
17. Y. Fan, and Q. Li Consistent model specification tests omitted variables and semiparametric functional forms Econometrica 64 1996 865 890
18. J.Q. Fan, and S.K. Lin Test of significance when data are curves Journal of the American Statistical Association 93 1998 1007 1021
19. J.H. Friedman, and R.J. Tibshirani The monotone smoothing of scatterplots Technometrics 26 1984 243 250
20. I. Gijbels, P. Hall, M.C. Jones, and I. Koch Tests for monotonicity of a regression mean with guaranteed level Biometrika 87 2000 663 673
21. P. Gozalo, and O. Linton Testing additivity in generalized nonparametric regression models Journal of Econometrics 104 2001 1 48
22. W. Härdle, and E. Mammen Comparing nonparametric vs parametric regression fits Annals of Statistics 21 1993 1926 1947
23. W. Härdle, P. Hall, and H. Ichimura Optimal smoothing in single-index models Annals of Statistics 21 1993 157 178
24. P. Hall, and J.D. Hart Bootstrap test for difference between means in nonparametric regression Journal of the American Statistical Association 85 1990 1039 1049
25. P. Hall, and N.E. Heckman Testing for monotonicity of a regression mean by calibrating for linear functions Annals of Statistics 28 2000 20 39
26. Hall, P., Huang, L.-S. 2001. Nonparametric kernel regression subject to monotonicity constraints. Annals of Statistics, to appear.
27. P. Hall, C. Huber, and P.L. Speckman Covariate-matched one-sided tests for the difference between functional means Journal of the American Statistical Association 92 1997 1074 1083
28. J. Hart Nonparametric Smoothing and Lack-of-Fit Tests 1997 Springer New York
29. T. Hastie, and R. Tibshirani Generalized Additive Models 1991 Chapman & Hall London
30. Y. Hong, and H. White Consistent specification testing via nonparametric series regression Econometrica 63 1995 1133 1160
31. J. Horowitz, and W. Härdle Testing a parametric model against a semiparametric alternative Econometric Theory 10 1994 821 848
32. J. Horowitz, and V. Spokoiny An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative Econometrica 69 2001 599 631
33. H. Ichimura Semiparametric least squares (SLS) and weighted SLS estimation of single-index models Journal of Econometrics 58 1993 71 120
34. T. Inglot, W.C.M. Kallenberg, and T. Ledwina Power approximations to and power comparison of smooth goodness-of-fit tests Scandinavian Journal of Statistics 21 1994 131 145
35. T. Inglot, W.C.M. Kallenberg, and T. Ledwina Vanishing shortcoming and asymptotic relative efficiency Annals of Statistics 28 2000 215 238
36. Y.I. Ingster Minimax distinguishability of families of nonparametric hypotheses Doklady Akademii Nauk SSSR (Russian) 267 1982 536 539
37. Y.I. Ingster Asymptotically minimax hypothesis testing for nonparametric alternatives. I Mathematical Methods of Statistics 2 1993 85 114 Erratum Mathematical Methods of Statistics 2, 268
38. Y.I. Ingster Asymptotically minimax hypothesis testing for nonparametric alternatives. II Mathematical Methods of Statistics 2 1993 171 189 Erratum Mathematical Methods of Statistics 2, 268
39. C. Kelly, and J. Rice Monotone smoothing with application to dose-response curves and the assessment of synergism Biometrics 46 1990 1071 1085
40. Kendall, M., Stuart, A., 1979. The Advanced Theory of Statistics, vol. 2, fourth edn. Griffin, London.
41. E. King, J.D. Hart, and T.E. Wehrly Testing the equality of two regression curves using linear smoothers Statistics and Probability Letters 12 1991 239 247
42. R. Klein, and R. Spady An efficient semiparametric estimator for binary response models Econometrica 61 1993 387 422
43. H.L. Koul, and A. Schick Testing for the equality of two nonparametric regression curves Journal of Statistical Planning and Inference 65 1997 293 314
44. K.B. Kulasekera, and J. Wang Smoothing parameter selection for power optimality in testing of regression curves Journal of the American Statistical Association 92 1997 500 511
45. P. Lavergne, and Q. Vuong Nonparametric significance testing Econometric Theory 16 2000 576 601
46. O. Lepski, and V. Spokoiny Minimax nonparametric hypothesis testing the case of an inhomogeneous alternative Bernoulli 5 1999 333 358
47. Q. Li, and S. Wang A simple consistent bootstrap test for a parametric regression function Journal of Econometrics 87 1998 145 165
48. O.B. Linton Efficient estimation of additive nonparametric regression models Biometrika 84 1997 469 474
49. O.B. Linton, and J.P. Nielsen A kernel method of estimating structured nonparametric regression based on marginal integration Biometrika 82 1995 93 100
50. E. Mammen Estimating a smooth monotone regression function Annals of Statistics 19 1991 724 740
51. E. Mammen, and C. Thomas-Agnan Smoothing splines and shape restrictions Scandinavian Journal of Statistics 26 1999 239 252
52. A. Pagan, and A. Ullah Nonparametric Econometrics 1999 Cambridge University Press Cambridge
53. J.L. Powell, J.H. Stock, and T.M. Stoker Semiparametric estimation of index coefficients Econometrica 57 1989 1403 1430
54. J.O. Ramsay Estimating smooth monotone functions Journal of the Royal Statistical Society Series B 60 1998 365 375
55. P.M. Robinson Root- n consistent semiparametric regression Econometrica 56 1988 931 954
56. W. Schlee Nonparametric tests of the monotony and convexity of regression B.V. Gnedenko M.L. Puri I. Vincze Nonparametric Statistical Inference vol. II 1982 North-Holland Amsterdam 823 836
57. P. Speckman Kernel smoothing in partial linear models Journal of the Royal Statistical Society Series B 50 1988 413 446
58. V. Spokoiny Adaptive hypothesis testing using wavelets Annals of Statistics 24 1996 2477 2498
59. C. Stone Additive regression and other nonparametric models Annals of Statistics 13 1985 685 705
60. M. Villalobos, and G. Wahba Inequality-constrained multivariate smoothing splines with application to the estimation of posterior probabilities Journal of the American Statistical Association 82 1987 239 248
61. M.P. Wand, and M.C. Jones Kernel Smoothing 1995 Chapman & Hall London
62. J. Wooldridge A test for functional form against nonparametric alternatives Econometric Theory 8 1992 452 475
63. I. Wright, and E. Wegman Isotonic, convex and related splines Annals of Statistics 8 1980 1023 1035
64. C. Wu Jackknife bootstrap and other resampling methods in regression analysis Annals of Statistics 14 1986 1261 1351
65. A. Yatchew Nonparametric regression model tests based on least squares Econometric Theory 8 1992 435 451
66. A. Yatchew Nonparametric regression techniques in economics Journal of Economic Literature XXXVI 1998 669 721
67. A. Yatchew An elementary nonparametric differencing test of equality of regression functions Economics Letters 62 1999 271 278
68. A. Yatchew, and L. Bos Nonparametric regression and testing in economic models Journal of Quantitative Economics 13 1997 81 131
69. A. Yatchew, Y. Sun, and C. Deri Efficient estimation of semiparametric equivalence scales with evidence from South Africa Journal of Business and Economics Statistics 21 2003 247 257
70. J.X. Zheng A consistent test of functional form via nonparametric estimation techniques Journal of Econometrics 75 1996 263 289