Testing a regression model when we have smooth alternatives in mind

Scandinavian Journal of Statistics

Volumn 26, Issue 2, 1999, Pages 221-238

  Härdle, Wolfgang ^b   Kneip, Alois ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b NONE

Author keywords

Goodness of fit tests; Regression models; Smooth alternatives

Indexed keywords

EID: 0033149329     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00146     Document Type: Article

References (28)

1. Azzalini, A., Bowman, A. W. & Härdle, W. (1989). On the use of nonparametric regression for model checking. Biometrika 76, 1-11.
2. Cox, D., Koh, E., Wahba, G. & Yandell, B. S. (1988). Testing the (parametric) null hypothesis in (semiparametric) partial and generalized spline models. Ann. Statist. 16, 113-119.
3. Deaton, A. S. (1981). Three essays on a Sri Lankan household survey. Living Standards Measurement Study W. D. No. 11, The World Bank, Washington.
4. Deaton, A. (1986). Demand analysis in Handbook of econometrics, (eds Z. Grilliches & M. D. Intrilligator), Vol. 3, 1777-1837. North Holland, New York.
5. de Boor, C. (1978). A practical guide to splines, Springer, New York.
6. Department of Employment (1969-1984). FES, Family expenditure survey, reports for 1968-1983. HMSO, London.
7. Devore, R. & Lorentz, G. (1991). Constructive approximation. Springer, New York.
8. Durbin, J. & Knott, M. (1972). Components of Cramér-von Mises statistics. J. Roy. Statist. Soc. Ser. B 34, 290-307.
9. Engel, E. (1857). Die Produktions-und Consumptionsverhältnisse des Königreichs Sachsen. Reprinted 1895 in: Bull. Inst. Internl. Statist. 9, 1-54.
10. Eubank, R. L. & Spiegelmann, C. H. (1990). Testing the goodness of fit of a linear model via nonparametric regression techniques. J. Amer. Statist. Assoc. 85, 387-392.
11. Fan, J. & Gijbels, I. (1996). Local polynomial modelling and its applications. Chapman & Hall, London.
12. Gasser, Th. & Müller, H. G. (1984). Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist. 11, 171-185.
13. Gasser, Th., Sroka, L. & Jennen-Steinmetz, C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika 73, 625-633.
14. Hall, P., Hart, J. D. & Titterington, D. M. (1990). Bootstrap test for difference between means in nonparametric regression. J. Amer. Statist. Assoc. 85, 1039-1049.
15. Hall, P., Kay, J. M. & Titterington, D. M. (1990). Asymptotically optimal difference based estimation of variance in nonparametric regression. Biometrika, 77, 521-529.
16. Härdle, W. & Mammen, E. (1993). Comparing nonparametric versus parametric fits. Ann. Statist. 21, 1926-1947.
17. Hart, J. D. (l 997). Nonpammetric smoothing and lack-of-fit tests. Springer, New York.
18. Hastie, T. J. & Tibshirani, R. J. (1990). Generalized additive models. Chapman & Hall, London.
19. Hong (1993). Consistent specification testing using optimal nonparametric kernel estimation. Center for Analytical Economics Working Paper No. 93-13, Cornell University.
20. Ingster, Y. I. (1982). Minimax nonparametric detection of signals in white Gaussian noise. Problems Inform. Transmission 18, 130-140.
21. Kneip, A. (1994). Ordered linear smoothers. Ann. Statist. 22, 835-866.
22. Leser, C. E. V. (1963). The form of Engel functions. Econometrica 31, 694-703.
23. L, cross-validation and generalized cross-validation: discrete index set. Ann. Statist. 15, 958-976.
24. P. Technometrics 15, 661-675.
25. Raz, J. (1990). Testing for no effect when estimating a smooth function by nonparametric regression: a randomization approach. J. Amer. Statist. Assoc. 85, 132-138.
26. Rice, J. A. (1984). Bandwidth choice for nonparametric regression. Ann. Statist. 12, 1215-1231.
27. Schumaker, L. L. (1990). Spline functions. Wiley, New York.
28. Working, H. (1943). Statistical laws of family expenditure. J. Amer. Statist. Assoc. 38, 43-56.