Adaptive tests of regression functions via multiscale generalized likelihood ratios

Canadian Journal of Statistics

Volumn 31, Issue 2, 2003, Pages 151-171

  Zhang, Chunming M ^a  

^a University of Wisconsin   (United States)

Author keywords

Adaptive Neyman test; Bandwidth selection; Generalized likelihood ratio; Local polynomial regression; Nonparametric test

Indexed keywords

EID: 0242427746     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316065     Document Type: Article

References (37)

1. R. J. Adler (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics Lecture Notes - Monograph Series 12, Institute of Mathematical Statistics, Hayward, California.
2. A. Azzalini & A. W. Bowman (1993). On the use of nonparametric regression for checking linear relationships. Journal of the Royal Statistical Society Series B, 55, 549-557.
3. A. Azzalini, A. W. Bowman & W. Härdle (1989). On the use of nonparametric regression for model checking. Biometrika, 76, 1-11.
4. C. Bellver (1987). Influence of particulate pollution on the positions of neutral points in the sky in Seville (Spain). Atmospheric Environment, 21, 699-702.
5. A. W. Bowman & S. G. Young (1996). Graphical comparison of nonparametric curves. Applied Statistics, 45, 83-98.
6. W. S. Cleveland (1993). Visualizing Data. Hobart Press, Summit, NJ.
7. A. Diblasi & A. W. Bowman (1997). Testing for constant variance in a linear model. Statistics & Probability Letters, 33, 95-103.
8. J. Fan (1996). Test of significance based on wavelet thresholding and Neyman's truncation. Journal of the American Statistical Association, 91, 674-688.
9. J. Fan & I. Gijbels (1995). Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. Journal of the Royal Statistical Society Series B, 57, 371-394.
10. J. Fan & I. Gijbels (1996). Local Polynomial Modeling and Its Applications. Chapman & Hall, London.
11. J. Fan & L. S. Huang (2001). Goodness-of-fit tests for parametric regression models. Journal of the American Statistical Association, 96, 640-652.
12. J. Fan & Q. Yao (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika, 85, 645-660.
13. J. Fan, C. M. Zhang & J. Zhang (2001). Generalized likelihood ratio statistics and Wilks phenomenon. The Annals of Statistics, 29, 153-193.
14. W. Feller (1966). An Introduction to Probability and Its Applications, Volume II. Wiley, New York.
15. D. Firth, J. Glosup & D. Hinkley (1991). Model checking with nonparametric curves. Biometrika, 78, 245-252.
16. T. Gasser & H. G. Müller (1979). Kernel estimation of regression functions. In Smoothing Techniques for Curve Estimation (T. Gasser and M. Rosenblatt, eds.), Springer, New York, pp. 23-68.
17. G. H. Golub & C. F. Van Loan (1996). Matrix Computations, Third edition. Johns Hopkins University Press, Baltimore, MD.
18. S. S. Gupta (1963). Probability integrals of multivariate normal and multivariate t. The Annals of Mathematical Statistics, 34, 792-828.
19. W. Härdle & E. Mammen (1993). Comparing nonparametric versus parametric regression fits. The Annals of Statistics, 21, 1926-1947.
20. J. D. Hart (1997). Nonparametric Smoothing and Lack-of-Fit Tests. Springer, New York.
21. J. D. Hart & T. S. Wehrly (1992). Kernel regression when the boundary region is large, with application to testing the adequacy of polynomial model. Journal of the American Statistical Association, 87, 1018-1024.
22. L. S. Huang (1997). Testing goodness-of-fit based on a roughness measure. Journal of the American Statistical Association, 92, 1399-1402.
23. Yu. I. Ingster (1982). Minimax nonparametric detection of signals in white Gaussian noise. Problems of Information Transmission, 18, 130-140.
24. G. Kauermann & G. Tutz (1999). On model diagnostics using varying coefficient models. Biometrika, 86, 119-128.
25. E. King, J. D. Hart & T. E. Wehrly (1991). Testing the equality of two regression curves using linear smoothers. Statistics & Probability Letters, 12, 239-247.
26. O. V. Lepski & V. G. Spokoiny (1999). Minimax nonparametric hypothesis testing: the case of an inhomogeneous alternative. Bernoulli, 5, 333-358.
27. J. Raz (1990). Testing for no effect when estimating a smooth function by nonparametric regression: a randomization approach. Journal of the American Statistical Association, 85, 132-137.
28. J. Rice (1984). Boundary modification in kernel regression. Communications in Statistics, Theory and Methods, 13, 893-900.
29. D. Ruppert, S. J. Sheather & M. P. Wand (1995). An effective bandwidth selector for local least squares regression. Journal of the American Statistical Association, 90, 1257-1270.
30. M. Stone (1974). Cross-validatory choice and assessment of statistical predictions (with discussion). Journal of the Royal Statistical Society Series B, 36, 111-147.
31. J. Y. Sun (1993). Tail probabilities of the maxima of Gaussian random fields. The Annals of Probability, 21, 34-71.
32. G. Wahba (1977). A survey of some smoothing problems and the method of generalized cross-validation for solving them. In Applications of Statistics (P. R. Krisnaiah, ed.), North Holland, Amsterdam, pp. 507-523.
33. 1 approximation for evaluation of multivariate normal integrals. Mathematica Numerica Sinica, 19, 91-102.
34. S. G. Young & A. W. Bowman (1995). Non-parametric analysis of covariance. Biometrics, 51, 920-931.
35. C. M. Zhang (2000). Topics in Generalized Likelihood Ratio Test. Unpublished doctoral thesis, Department of Statistics, University of North Carolina, Chapel Hill, NC.
36. C. M. Zhang (2001). Equivalent nonparametric regression tests based on spline and local polynomial smoothers. Technical Report, Department of Statistics, University of Wisconsin, Madison, WI.
37. C. M. Zhang & B. Cheng (2003). Binning methodology for nonparametric goodness-of-fit test. Journal of Statistical Computation and Simulation, 73, 71-82.