Simultaneous inference of linear models with time varying coefficients

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 72, Issue 4, 2010, Pages 513-531

  Zhou, Zhou ^a   Wu, Wei Biao ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Functional linear models; Gaussian approximation; Local linear regression; Local stationarity; Non parametric goodness of fit tests; Non stationary time series; Simultaneous confidence tubes

Indexed keywords

EID: 78650349691     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2010.00743.x     Document Type: Article

References (34)

1. Bickel, P. J. and Rosenblatt, M. (1973) On some global measures of the deviations of density function estimates. Ann. Statist., 1, 1071-1095.
2. Cai, Z. (2007) Trending time-varying coefficient time series models with serially correlated errors. J. Econometr., 136, 163-188.
3. Cai, Z., Fan, J. and Li, R. Z. (2000) Efficient estimation and inferences for varying-coefficient models. J. Am. Statist. Ass., 95, 888-902.
4. Craven, P. and Wahba, G. (1979) Smoothing noisy data with spline functions. Numer. Math., 31, 377-403.
5. Dahlhaus, R. (1997) Fitting time series models to non-stationary processes. Ann. Statist., 25, 1-37.
6. Doukhan, P. and Louhichi, S. (1999) A new weak dependence condition and applications to moment inequalities. Stoch. Processes Appl., 84, 313-342.
7. Draghicescu, D., Guillas, S. and Wu, W. B. (2009) Quantile curve estimation and visualization for nonstationary time series. J. Comput. Graph. Statist., 18, 1-20.
8. Eubank, R. L. and Speckman, P. L. (1993) Confidence bands in nonparametric regression. J. Am. Statist. Ass., 88, 1287-1301.
9. Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and Its Applications. New York: Chapman and Hall.
10. Fan, J. and Huang, T. (2005) Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli, 11, 1031-1057.
11. Fan, J. and Zhang, W. Y. (1999) Statistical estimation in varying coefficient models. Ann. Statist., 27, 1491-1518.
12. Fan, J. and Zhang, W. Y. (2000) Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scand. J. Statist., 27, 715-731.
13. Hall, P. (1991) On the distribution of suprema. Probab. Theor. Reltd Flds, 89, 447-455.
14. Härdle, W. and Marron, J. S. (1991) Bootstrap simultaneous error bars for nonparametric regression. Ann. Statist., 19, 778-796.
15. 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.
16. Huang, J. Z., Wu, C. O. and Zhou, L. (2004) Polynomial spline estimation and inference for varying coefficient models with longitudinal data. Statist. Sin., 14, 763-788.
17. Johnston, G. J. (1982) Probabilities of maximal deviations for nonparametric regression function estimates. J. Multiv. Anal., 12, 402-414.
18. Lin, D. Y. and Ying, Z. (2001) Semiparametric and nonparametric regression analysis of longitudinal data (with discussion). J. Am. Statist. Ass., 96, 103-126.
19. 2-process and other functions of multidimensional gaussian processes, with reliability applications. Adv. Appl. Probab., 12, 746-774.
20. Liu, W. and Lin, Z. (2009) Strong approximation for a class of stationary processes. Stoch. Processes Appl., 119, 249-280.
21. Neumann, M. H. and Kreiss, J. P. (1998) Regression-type inference in nonparametric autoregression. Ann. Statist., 26, 1570-1613.
22. Neumann, M. H. and Polzehl, J. (1998) Simultaneous bootstrap confidence bands in nonparametric regression. J. Nonparam. Statist., 9, 307-333.
23. Orbe, S., Ferreira, E. and Rodriguez-Poo, J. (2005) Nonparametric estimation of time varying parameters under shape restrictions. J. Econometr., 126, 53-77.
24. Orbe, S., Ferreira, E. and Rodriguez-Poo, J. (2006) On the estimation and testing of time varying constraints in econometric models. Statist. Sin., 16, 1313-1333.
25. Politis, D. N., Romano, J. P. and Wolf, M. (1999) Subsampling. New York: Springer.
26. Ramsay, J. and Silverman, B. W. (2005) Functional Data Analysis. New York: Springer.
27. Robinson, P. M. (1989) Nonparametric estimation of time-varying parameters. In Statistical Analysis and Forecasting of Economic Structural Change (ed. P. Hackl ), pp. 164-253. Berlin: Springer.
28. Robinson, P. M. (1991) Time-varying nonlinear regression. In Economic Structure Change Analysis and Forecasting (eds P. Hackl and A. H. Westland ), pp. 179-190. Berlin: Springer.
29. Wu, W. B. (2005) Nonlinear system theory: another look at dependence. Proc. Natn. Acad. Sci. USA, 102, 14150-14154.
30. Wu, W. B. (2007) Strong invariance principles for dependent random variables. Ann. Probab., 35, 2294-2320.
31. Wu, C. O., Chiang, C. T. and Hoover, D. R. (1998) Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data. J. Am. Statist. Ass., 93, 1388-1402.
32. Wu, W. B. and Zhao, Z. (2007) Inference of trends in time series. J. R. Statist. Soc. B, 69, 391-410.
33. Wu, W. B. and Zhou, Z. (2009) Gaussian approximations for non-stationary multiple time series. Statist. Sin., to be published.
34. Zhou, Z. and Wu, W. B. (2009) Local linear quantile estimation of nonstationary time series. Ann. Statist., 37, 2696-2729.