Local linear estimation in partly linear models

Journal of Multivariate Analysis

Volumn 60, Issue 1, 1997, Pages 1-19

  Hamilton, Scott A ^a   Truong, Young K ^a  

^a NONE

Author keywords

Design adaptive; Local polynomial estimator; Nonparametric regression; Optimal rate of convergence; Partial linear models; Semi parametric models

Indexed keywords

EID: 0030642401     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.1642     Document Type: Article

References (26)

1. [1] Chen, H. (1988). Convergence rates for parametric components in a partly linear model. Ann. Statist. 16 136-146.
2. [2] Chen, H., and Shiau, J.-J. H. (1991). A two-stage spline smoothing method for partially linear models. J. Statist. Planning Inference 27 187-202.
3. [3] Chen, H., and Shiau, J.-J. H. (1994). Data-driven efficient estimation for a partially linear model. Ann. Statist. 22 211-237.
4. [4] Denby, L. (1986). Smooth regression function. Statistical Research Report 26. AT&T Bell Laboratories, Princeton, New Jersey.
5. [5] Engle, R., Granger, C., Rice, J., and Weiss, A. (1986). Nonparametric estimates of the relation between weather and electricity sales. J. Amer. Statist. Assoc. 81 310-320.
6. [6] Eubank, R. L., and Whitney, P. (1989). Convergence rates for estimation in certain partially linear models. J. Statist. Planning Inference 23 33-43.
7. [7] Eubank, R. L., Hart, J. D., and Speckman, P. (1990). Trigonometric series regression estimators with an application to partially linear models. J. Multivariate Anal. 32 70-83.
8. [8] Fan, J. (1992). Design adaptive nonparametric function estimation: A unified approach, J. Amer. Statist. Assoc. 87 998-1004.
9. [9] Fan, J. (1993). Local linear regression smoothers and their minimax efficiency. Ann. Statist. 21 196-216.
10. [10] Fan, J., and Gijbels, I. (1992). Variable bandwidth and local linear regression smoothers. Ann. Statist. 20 2008-2036.
11. [11] Fan, J., Hu, T., and Truong, Y. K. (1994). Robust non-parametric function estimation. Scand. J. Statist. 21 433-446.
12. [12] Green, P., Jennison, C, and Seheult, A. (1985). Analysis of field experiments by least squares smoothing. J. Royal Statist. Soc. Ser. B. 47 299-315.
13. [13] Heckman, N. E. (1986). Spline smoothing in a partly linear model. J. Royal Statist. Soc. Ser. B. 48 244-248.
14. [14] Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 13-30.
15. [15] Rice, J. (1986). Convergence rates for partially splined models. Statist. Probabil. Lett. 4 203-208.
16. [16] Ruppert, D., and Wand, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22 1346-1370.
17. [17] Schelfé, H. (1959). The Analysis of Variance. Wiley, New York.
18. [18] Shiau, J., Wahba, G., and Johnson, D. R. (1986). Partial spline models for the inclusion of tropopause and frontal boundary information in otherwise smooth two and three dimensional objective analysis. J. Atmospheric Oceanic Technol. 3 714-725.
19. [19] Speckman, P. (1988). Kernel smoothing in partial linear models. J. Royal Statist. Soc. Ser. B 50 413-436.
20. [20] Stone, C. J. (1977). Consistent nonparametric regression. Ann. Statist. 5 595-645.
21. [21] Stone, C. J. (1980). Optimal rates of convergence for nonparametric estimators. Ann. Statist. 8 1348-1360.
22. [22] Stone, C. J. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10 1040-1053.
23. [23] Stone, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation (with discussion). Ann. Statist. 22 118-184.
24. [24] Truong, Y. K., and Stone, C. J. (1994). Semiparametric time series regression. J. Time Series Anal. 15 405-428.
25. [25] Wahba, G. (1984). Partial spline models for the semiparametric estimation of functions of several variables. In Statistical Analysis of Time Series, Japan-US Joint Sem., pp. 312-329. Institute of Statistical Mathematics. Tokyo.
26. [26] Wand, W. P., and Jones, M. C. (1993). Comparison of smoothing parameterizations in bivariate kernel density estimation. J. Amer. Statist. Assoc. 88 520-528.