Local linear smoothers using asymmetric kernels

Annals of the Institute of Statistical Mathematics

Volumn 54, Issue 2, 2002, Pages 312-323

  Chen, Song Xi ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Beta kernels; Gamma kernels; Local linear smoother; Non parametric regression; Sparse region

Indexed keywords

MATRIX ALGEBRA; PARAMETER ESTIMATION; POLYNOMIALS; THEOREM PROVING;

NONPARAMETRIC REGRESSION;

REGRESSION ANALYSIS;

EID: 6444244671     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022422002138     Document Type: Article

References (16)

1. Abramson, I. S. (1982). On bandwidth variation in kernel estimates - a square root law, Ann. Statist., 10, 1217-1223.
2. Brown, B. M. and Chen, S. X. (1999). Beta-Bernstein smoothing for regression curves with compact supports, Scand. J. Statist., 26, 47-59.
3. Chen, S. X. (2000a). Beta kernel smoother for regression curves, Statist. Sinica, 10, 73-91.
4. Chen, S. X. (2000b). Probability density function estimation using gamma kernels, Ann. Inst. Statist. Math., 52, 471-480.
5. Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots, J. Amer. Statist. Assoc., 74, 829-836.
6. Cleveland, W. S. and Devlin, S. (1988). Locally weighted regression: An approach to regression analysis by local fitting, J. Amer. Statist. Assoc., 83, 596-610.
7. Fan, J. Q. (1993). Local linear regression smoothers and their minimax efficiencies, Ann. Statist., 21, 196-216.
8. Fan, J. Q. and Gijbels, I. (1992). Variable bandwidth and local linear regression smoothers, Ann. Statist., 20, 2008-2036.
9. Fan, J. Q. and Gijbels, I. (1996) Local Polynomial Modeling and Its Applications, Chapman and Hall, London.
10. Hall, P. and Turlach, B. A. (1997). Interpolation methods for adapting to sparse design in nonparametric regression (with discussion), J. Amer. Statist. Assoc., 92, 466-476.
11. Hastie, T. and Loader, C. (1993). Local regression: Automatic kernel carpentry, Statist. Sci., 8, 120-143.
12. Ruppert, D. and Wand, M.P. (1994). Multivariate locally weighted least squares regression, Ann. Statist., 22, 1346-1370.
13. Seifert, B. and Gasser, Th. (1996a). Finite sample variance of local polynomials: Analysis and solutions, J. Amer. Statist. Assoc., 91, 267-275.
14. Seifert, B. and Gasser, Th. (1996b). Variance properties of local polynomials and ensuring modifications (with discussion), Statistical Theory and Computational Aspects of Smoothing (eds. W. Härdle and M. G. Schimek), 5-79, Physica, Heidelberg.
15. Stone, C. J. (1977). Consistent nonparametric regression, Ann. Statist., 5, 595-645.
16. Press, W. H., Flannery, B. F., Teukolsky, S. A. and Vetterling, W. T. (1992). Numerical Recipes inC. The Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge.