Structural tests in additive regression

Journal of the American Statistical Association

Volumn 96, Issue 456, 2001, Pages 1333-1347

  Härdle, Wolfgang ^a   Sperlich, Stefan ^b   Spokoiny, Vladimir ^c  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^c WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Additive model; Component analysis; Haar basis; Hypothesis testing; Nonparametric alternative; Regression

Indexed keywords

EID: 1542679202     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1198/016214501753382264     Document Type: Article

References (41)

1. Aerts, M., Claesken, G., and Hart, J. D. (1999), “Testing the Fit of a Parametric Function,” Journal of the American Statistical Association, 94, 869-879.
2. Bierens, H. J. (1982), “Consistent Model Specification Tests,” Journal of Econometrics, 20, 105-134.
3. Blundell, R., Duncan, A., and Meghir, C. (1998), “Estimating Labor Supply Responses Using Tax Reforms,” Econometrica, 4, 827-861.
4. Buja, A., Hastie, T. J., and Tibshirani, R. J. (1989), “Linear Smoothers and Additive Models,” The Annals of Statistics, 17, 453-555.
5. Burnashev, M. V. (1979), “On the Minimax Detection of an Inaccurately Known Signal in a White Gaussian Noise Background,” Theory of Probability and Applications, 24, 107-119.
6. Deaton, A., and Muellbauer, J. (1980), Economics and Consumer Behavior, New York: Cambridge University Press.
7. Eubank, R. L., and Hart, J. D. (1992), “Testing Goodness of Fit in Regression via Order Selection Criteria,” The Annals of Statistics, 20, 1412-1425.
8. Fan, J. (1996), “Test of Significance Based on Wavelet Thresholding and Neyman’s Truncation,” Journal of the American Statistical Association, 91, 674-688.
9. Fan, J., and Huang, L. (1998), “Goodness-of-Fit Test for Parametric Regression Models,” preprint, University of North Carolina http://www.unc.edu/depts/statistics/faculty/fan/
10. Gasser, T., Sroka, L., and Jennen-Steinmetz, C. (1986), “Residual Variance and Residual Pattern in Nonlinear Regression,” Biometrika, 73, 625-633.
11. Hall, P., Kay, J. W., and Titterington, D. M. (1990), “Asymptotically Optimal Differences-Based Estimation of Variance in Nonparametric Regression,” Biometrika, 77, 521-528.
12. Hall, P., Kay, J. W., and Titterington, D. M. (1991), “On Estimation of Noise Variance in Two-Dimensional Signal Processing,” Advances in Applied Probability, 23, 476-495.
13. Härdle, W., and Korostelev, A. (1996), “Search of Significant Variables in Nonparametric Additive Regression,” Biometrika, 83, 541-549.
14. Härdle, W., and Mammen, E. (1993), “Comparing Nonparametric Versus Parametric Regression Fits,” The Annals of Statistics, 21, 1926-1947.
15. Härdle, W., Sperlich, S., and Spokoiny, V. (1997), Component Analysis for Additive Models,” SFB Discussion Paper 52, Humboldt University, Berlin.
16. Hart, J. D. (1997), Nonparametric Smoothing and Lack-of-Fit Tests, New York: Springer.
17. Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, New York: Chapman and Hall.
18. Horowitz, J., and Spokoiny, V. (1999), “On Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative,” Econometrica, 69, 599-631.
19. Inglot, T., and Ledwina, T. (1996), “Asymptotic Optimality of Data-Driven Neyman’s tests for Uniformity,” The Annals of Statistics, 24, 1982-2019.
20. Ingster, Yu. I. (1982), “Minimax Nonparametric Detection of Signals in White Gaussian Noise,” Problems of Information Transmission, 18, 130-140.
21. Ingster, Yu. I. (1993), “Asymptotically Minimax Hypothesis Testing for Nonparametric Alternatives, I-III,” Mathematical Methods of Statistics, 2, 85-114; 3, 171-189; 4, 249-268.
22. Kallenberg, W. C. M., and Ledwina, T. (1995), “Consistency and Monte-Carlo Simulations of a Data-Driven Version of Smooth Goodness-of-Fit Tests,” The Annals of Statistics, 23, 1594-1608.
23. Ledwina, T. (1994), “Data-Driven Version of Neyman’s Smooth Test of Fit,” Journal of the American Statistical Association, 89, 1000-1005.
24. Leontief, W. (1947), “Introduction to a Theory of the Internal Structure of Functional Relationships,” Econometrica, 15, 361-373.
25. Linton, O. B., and Nielsen, J. P. (1995), “A Kernel Method of Estimating Structured Nonparametric Regression Based on Marginal Integration,” Biometrika, 82, 93-100.
26. p ,” Technometrics, 15, 661-675.
27. Mroz, T. A. (1987), “The Sensitivity of an Empirical Model of Married Women’s Hours of Work to Economic and Statistical Assumptions,” Econometrica, 55, 765-800.
28. Rice, J. (1984), “Bandwidth Choice for Nonparametric Regression,” The Annals of Statistics, 12, 1215-1230.
29. Sperlich, S. (1998), Additive Modelling and Testing Model Specification, Aachen: Shaker.
30. Sperlich, S., Tøstheim, D., and Yang, L. (1999), “Nonparametric Estimation and Testing of Interaction in Additive Models,” Working Paper 99-85 (34), Universidad Carlos III de Madrid, Spain.
31. Spokoiny, V. (1996), “Adaptive Hypothesis Testing Using Wavelets,” The Annals of Statistics, 24, 2477-2498.
32. Spokoiny, V. (1998), “Adaptive and Spatially Adaptive Testing of a Nonparametric Hypothesis,” Mathematical Methods of Statistics, 7, 245-273.
33. Spokoiny, V. (1999a), “Data-Driven Testing the Fit of Linear Models,” Preprint 471, Weierstrass-Institute, Berlin.
34. Spokoiny, V. (1999b), “Variance Estimation for High-Dimensional Regression Models,” Preprint 503, Weierstrass-Institute, Berlin.
35. Stone, C. J. (1985), “Additive Regression and Other Nonparametric Models,” The Annals of Statistics, 13, 689-705.
36. Stone, C. J. (1986), “The Dimensionality Reduction Principle for Generalized Additive Models,” The Annals of Statistics, 14, 590-606.
37. Strøm, St., and Wagenhals, G. (1991), “Female Labour Supply in the Federal Republik,” Jahrbuch für Nationalökonomie und Statistik, 208(6), 575-595.
38. Stute, W. (1997), “Nonparametric Model Checks for Regression,” The Annals of Statistics, 25, 613-641.
39. Tjøstheim, D., and Auestad, B. H. (1994), “Nonparametric Identification of Nonlinear Time Series: Projections,” Journal of the American Statistical Association, 89, 1398-1409.
40. Treiman, D. J. (1978), “Probleme der Begriffsbildung und Operationalisierung in der international vergleichenden Mobilitätsforschung,” in Sozialstrukturanalysen mit Umfragedaten, ed. F. U. Pappi, Kronberg im Taunus: Athenäum.
41. Venables, W. N., and Ripley, B. (1994), Modern Applied Statistics With S-PLUS, New York: Springer.