L1-estimation for varying coefficient models

Statistics

Volumn 39, Issue 5, 2005, Pages 389-404

  Tang, Qingguo ^a,b   Wang, Jinde ^a  

^a NANJING UNIVERSITY   (China)

^b PLA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

ACV bandwidth selection; Asymptotic normality; Least absolute deviation estimation; Varying coefficient model

Indexed keywords

EID: 29344458105     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331880500310165     Document Type: Article

References (29)

1. Cleveland, W.S., Grosse, E. and Shyu, W.M., 1992, Local regression models. In: J.M. Chambers and T.J. Hastie (Eds) Statistical Models in S (Pacific Grove: Wadsworth and Brooks), pp. 309-376.
2. Hastie, T.J. and Tibshirani, R.J., 1993, Varying coefficient models. Journal of the Royal Statistical Society Series B, 55, 757-796.
3. Carroll, R.J., Ruppert, D. and Welsh, A.H., 1998, Local estimating equations. Journal of American Statistical Association, 93, 214-227.
4. Kauermann, G. and Tutz, G., 1999, On model diagnostics using varying-coefficient models. Biometrika, 86, 119-128.
5. Xia, Y. and Li, W.K., 1999, On the estimation and testing of functional-coefficient linear models. Statistical Sinica, 9, 735-757.
6. Zhang, W. and Lee, S.Y., 2000, Variable bandwidth selection in varying-coefficient model. Journal of Multivariate Analysis, 74, 116-134.
7. Fan, J. and Zhang, W., 1999, Statistical estimation in varying coefficient models. Annals of Statistics, 27, 1491-1518.
8. Fan, J. and Zhang, J., 2000, Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society Series B, 62, 303-322.
9. Fan, J. and Zhang, W., 2000, Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scandinavian Journal of Statistics, 27, 715-731.
10. Eubank, R.L., Huang, C., Maldonado, Y.M., Wang, N., Wang, S. and Buchanan, R.J., 2004, Smoothing spline estimation in varying-coefficient models. Journal of the Royal Statistical Society Series B, 66, 653-667.
11. Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P., 1998, Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, 85, 809-822.
12. Wu, C.O., Chiang, C.T. and Hoover, D.R., 1998, Asymptotic confidence regions for kernelsmoothing of a varying-coefficient model with longitudinal data. Journal of American Statistical Association, 93, 1388-1402.
13. Huang, J.Z., Wu, C.O. and Zhou, L., 2002, Varying-coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika, 89, 111-128.
14. Cai, Z., Fan, J. and Yao, Q., 2000, Functional-coefficient regression models for nonlinear time series models. Journal of American Statistical Association, 95, 941-956.
15. Cai, Z., Fan, J. and Li, R., 2000, Efficient estimation and inferences for varying-coefficient models. Journal of American Statistical Association, 95, 888-902.
16. Fan, J., Yao, Q. and Cai, Z., 2003, Adaptive varying-coefficient linear models. Journal of the Royal Statistical Society Series B, 65, 57-80.
17. Chiang, C.T., Rice, J.A. and Wu, C.O., 2001, Smoothing spline estimation for varing coefficient models with repeatedly measured dependent variables. Journal of American Statistical Association, 96, 605-619.
18. Hardie, W., 1984, Robust regression function estimation. Journal of Multivariate Analysis, 14, 169-180.
19. Truong, Y.K., 1992, Robust nonparametric regression in time series. Journal of Multivariate Analysis, 41, 163-177.
20. 1 method for robust nonparametric regression. Journal of American Statistical Association, 89, 65-76.
21. Tukey, J.W., 1977, Exploratory Data Analysis (Reading, MA: Addison-Wesley).
22. Hardie, W., 1990, Applied Nonparametric Regression (Cambridge, UK: Cambridge University Press).
23. Silverman, B.W., 1986, Density Estimation for Statistics and Data Analysis (London: Chapman and Hall).
24. Rice, J.A. and Silverman, B.W., 1991, Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society Series B, 53, 233-243.
25. Pollard, D., 1991, Asymptotics for least absolute deviation regression estimators. Econometric Theory, 7, 186-199.
26. Prakasa, R.B.L.S., 1987, Asymptotic Theory of Statistical Inference (New York: John Wiley).
27. 1-estimators in nonlinear regression. Journal of Multivariate Analysis, 54, 227-238.
28. Wang, J., 1996, The asymptotics of least squares estimators for constrained nonlinear regression. Annals of Statistics, 24, 1316-1326.
29. Cox, D.D., 1983, Asymptotics for M-type smoothing splines. Annals of Statistics, 11, 530-551.