Local polynomial variance-function estimation

Technometrics

Volumn 39, Issue 3, 1997, Pages 262-273

  Ruppert, David ^a   Wand, M P ^b   Holst, Ulla ^c   HöSJER, Ola ^c  

^a Department of Materials Science and Engineering   (United States)

^b Australian Graduate School of Management   (Australia)

^c LUND UNIVERSITY   (Sweden)

Author keywords

Bandwidth; Heteroscedasticity; Kernel smoothing; Nonparametric regression; Smoother matrix

Indexed keywords

AIR POLLUTION; BANDWIDTH; CALCULATIONS; ESTIMATION; FUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; POLYNOMIALS;

HETEROSCEDASCITY; KERNEL SMOOTHING; LIGHT DETECTION AND RANGING METHOD; NONPARAMETRIC REGRESSION; SMOOTHER MATRIX; VARIANCE FUNCTIONS;

REGRESSION ANALYSIS;

EID: 0031199387     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1997.10485117     Document Type: Article

References (31)

1. Bickel, P. J. (1982), “On Adaptive Estimation,”The Annals of Statistics,10, 647-671
2. Buckley, M. J., Eagleson, G. K., and Silverman, B. W. (1988), “The Estimation of Residual Variance in Nonparametric Regression,”Biometrika,75, 189-200.
3. Carroll, R. J. (1982), “Adapting for Heteroscedasticity in Linear Models,”The Annals of Statistics,10, 1224-1233.
4. Carroll, R. J., and Ruppert, D. (1988), Transformation and Weighting in Regression, New York: Chapman &Hall.
5. Cleveland, W. (1979), “Robust Locally Weighted Regression and Smoothing Scatterplots,”Journal of the American Statistical Association,74, 829-836.
6. Cleveland, W., and Devlin, S. (1988), “Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting,”Journal of the American Statistical Association,83, 596-610.
7. Cleveland, W. S., and Loader, C. (1996), “Smoothing by Local Regression: Principles and Methods,” inStatistical Theory and Computational Aspects of Smoothing, eds. W. Härdle and M. G. Schimek, Heidelberg: Physica Verlag, pp. 101-149.
8. Dreeben, T. D., and Pope, S. B. (1995), “Pdf and Reynolds-stress Modeling of Near-wall Turbulent Flows.” unpublished manuscript.
9. Fan, J. (1992), “Design-Adaptive Nonparametric Regression,”Journal of the American Statistical Association,87, 998-1004.
10. Fan, J., and Gijbels, I. (1992), “Variable Bandwidth and Local Linear Regression Smoothers,”The Annals of Statistics,20, 2008-2038.
11. Fan, J., and Gijbels, I. (1995), “Data-driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth and Spatial Adaptation,”Journal of the Royal Statistical Society, Ser. B, 57, 371-394.
12. Fan, J., and Gijbels, I. (1996), Local Polynomial Modeling and Its Applications, London: Chapman &Hall.
13. Gasser, T., Sroka, L., and Jennen-Steinmetz, C. (1986), “Residual Variance and Residual Pattern in Nonlinear Regression,”Biometrika,73,625-634.
14. Hall, P., and Carroll, R. J. (1989), “Variance Function Estimation in Regression: The Effect of Estimating the Mean,”Journal of the Royal Statistical Society, Ser. B, 51, 3-14.
15. Hall, P., Kay, J. W., and Titterington, D. M. (1990), “Asymptotically Optimal Difference-Based Estimation of Variance in Nonparametric Regression,”Biometrika,77, 521-528.
16. Hastie, T. J., and Loader, C. (1993), “Local Regression: Automatic Kernel Carpentry” (with discussion), Statistical Science,8, 120-143.
17. Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, New York: Chapman &Hall.
18. Holst, U., Hössjer, O., Björklund, C., Ragnarson, P., and Edner, H. (1996), “Locally Weighted Least Squares Kernel Regression and Statistical Evaluation of LIDAR Measurements,”Environmetrics, 1,401-416.
19. Mathur, A. (1995), “On Estimation of Residual Variance Function,” paper presented at the Joint Statistical Meetings, Orlando, Florida, August 13-17.
20. McCullagh, P. (1987), Tensor Methods in Statistics, London: Chapman &Hall.
21. Müller, H. G., and Stadtmüller, U. (1987), “Estimation of Heteroscedasticity in Regression Analysis,”The Annals of Statistics,15, 610-625.
22. Pope, S. B. (1985), “Pdf Methods for Turbulent Reactive Flows,”Progress in Energy and Combustion Science,11,119-192.
23. Rice, J. (1984), “Bandwidth Choice for Nonparametric Regression,”The Annals of Statistics,12, 1215-1230.
24. Ruppert, D. (1995), “Empirical-Bias Bandwidths for Local Polynomial Nonparametric Regression and Density Estimation,” unpublishedmanuscript (TR 1137 athttp://www.orie.cornell.edu/trlist/trlist.html).
25. Ruppert, D., Sheather, S. J., and Wand, M. R (1995), “An Effective Bandwidth Selector for Local Least Squares Regression,”Journal of the American Statistical Association,90, 1257-1270.
26. Ruppert, D., and Wand, M. P. (1994), “Multivariate Locally Weighted Least Squares Regression,”The Annals of Statistics,22, 1346-1370.
27. Sigrist, M. (ed.) (1994), Air Monitoring by Spectroscopic Techniques(Chemical Analysis Series, Vol. 127), New York: Wiley.
28. Silverman, B. (1985), “Some Aspects of the Spline Smoothing Approach to Non-parametric Regression Curve Fitting” (with discussion), Journal of the Royal Statistical Society, Ser. B, 47, 1-52.
29. Stone, C. J. (1977), “Consistent Nonparametric Regression,”The Annals of Statistics,5, 595-620.
30. Turlach, B. A., and Wand, M. P. (1996), “Fast Computation of Auxiliary Quantities in Local Polynomial Smoothing,”Journal of Computational and Graphical Statistics,5, 337-350.
31. Wand, M. P., and Jones, M. C. (1995), Kernel Smoothing, London: Chapman &Hall