Interpolation methods for nonlinear wavelet regression with irregularly spaced design

Annals of Statistics

Volumn 25, Issue 5, 1997, Pages 1912-1925

  Hall, Peter ^a   Turlach, Berwin A ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Bias; Mean squared error; Nonparametric regression; Piecewise smooth; Stochastic design; Threshold; Variance

Indexed keywords

EID: 0031510620     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1069362378     Document Type: Article

References (18)

1. CAI, T. (1996). Noriparametric function estimation via wavelets. Ph.D. dissertation, Cornell Univ.
2. CHU, C.-K. and MARRON, J. S. (1991). Choosing a kernel regression estimator. Statist. Sci. 6 404-436.
3. CLARK, R. M. (1977). Nonparametric estimation of a smooth regression function. J. Roy. Statist. Soc. Ser. B 39 107-113.
4. CLARK, R. M. (1980). Calibration, cross-validation and carbon-14. II. J. Roy. Statist. Soc. Ser. A 143 177-194.
5. DONOHO, D. and JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455.
6. DONOHO, D. and JOHNSTONE, I. M. (1998). Minimax estimation via wavelet shrinkage. Unpublished manuscript.
7. DONOHO, D., JOHNSTONE, I. M., KERKYACHARIAN, G. and PICARD, D. (1996). Density estimation by wavelet thresholding. Ann. Statist. 24 508-539.
8. DONOHO, D., JOHNSTONE, I. M., KERKYACHARIAN, G. and PICARD, D. (1995). Wavelet shrinkage: asymptopia? (with discussion). J. Roy. Statist. Soc. Ser. B 57 301-369.
9. GASSER, TH. and MÜLLER, H.-J. (1979). Kernel estimation of regression functions. Smoothing Techniques for Curve Estimation. Lecture Notes in Math. 757 23-68. Springer, Heidelberg.
10. HALL, P. and PATIL, P. (1996a). On the choice of smoothing parameter, threshold and truncation in nonparametric regression by nonlinear wavelet methods. J. Roy. Statist. Soc. Ser. B 58 361-377.
11. HALL, P. and PATIL, P. (1996b). Effect of threshold rules on performance of wavelet-based curve estimators. Statist. Sinica 6 331-345.
12. HALL, P. and TURLACH, B. A. (1995). Interpolation methods for nonlinear wavelet regression with irregularly spaced design. Unpublished manuscript.
13. HÄRDLE, W. (1990). Applied Nonparametric Regression. Cambridge Univ. Press.
14. HASTIE, T. and LOADER, C. (1993). Local regression: automatic kernel carpentry. Statist. Sci. 8 120-143.
15. HOEFFDING, W. (1963). On sequences of sums of independent random variables. J. Amer. Statist. Assoc. 58 13-30.
16. KERKYACHARIAN, G. and PICARD, D. (1993). Density estimation by kernel and wavelet methods, optimality in Besov Spaces. Statist. Probab. Lett. 18 327-336.
17. NASON, G. P. and SILVERMAN, B. W. (1994). The discrete wavelet transform. J. Comput. Graph. Statist. 3 163-191.
18. WAND, M. P. and JONES, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.