Local linear regression estimation for time series with long-range dependence

Stochastic Processes and their Applications

Volumn 82, Issue 2, 1999, Pages 173-193

  Masry, Elias ^a   Mielniczuk, Jan ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b INSTITUTE OF COMPUTER SCIENCE   (Poland)

Author keywords

60F05; 62G05; Asymptotic distributions; Local linear regression estimation; Long range dependent errors; Random design nonparametric regression; Smoothing dichotomy

Indexed keywords

EID: 0003142774     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00015-0     Document Type: Article

References (22)

1. Castellana J.V., Leadbetter M.R. On smoothed probability density estimation. Stochastic Process. Appl. 21:1986;179-193.
2. Cheng B., Robinson P.M. Semiparametric estimation from time series with long-range dependence. J. Econometrics. 64:1994;335-353.
3. Csörgo S., Mielniczuk J. Density estimation under long-range dependence. Ann. Statist. 23:1995;990-999.
4. Csörgo, S., Mielniczuk, J., 1998. The smoothing dichotomy in random-design regression with long-memory errors based on moving averages. Technical Report #316. Dept. Stat., University of Michigan.
5. Csörgo, S., Mielniczuk, J., 1999. Random-design regression under long-range dependent errors. Bernoulli 5, 209-224.
6. Dobrushin R.L., Major P. Non-central limit theorems for non-linear functionals of Gaussian fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete. 50:1979;27-52.
7. Fan J. Design-adaptive nonparametric regression. J. Amer. Statist. Assoc. 87:1992;998-1004.
8. Fan J. Local linear regression smoothers and their minimax efficiency. Ann. Statist. 21:1993;196-216.
9. Fan J., Gijbels I. Variable bandwidth and local linear regression smoothers. Ann. Statist. 20:1992;2008-2036.
10. Fan, J., Gijbels, I., 1996. Local Polynomial Modelling and its Applications. Chapman and Hall, London.
11. Fan J., Masry E. Multivariate regression estimation with errors-in-variables: asymptotic normality for mixing processes. J. Multivariate Anal. 43:1992;237-271.
12. Hidalgo J. Nonparametric estimation with strongly dependent multivariate time series. J. Time Ser. Anal. 18:1997;95-122.
13. Koul H.L. M-estimators in linear models with long range dependent errors. Statist. Probab. Lett. 14:1992;153-164.
14. Koul H.L., Mukherjee K. Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors. Probab. Theory Related Fields. 95:1993;535-553.
15. Masry E. Multivariate local polynomial regression for time series: uniform consistency and rates. J. Time Ser. Anal. 17:1996;571-599.
16. Masry E. Multivariate regression estimation: local polynomial fitting for time series. J. Stochastic Processes Appl. 65:1996;81-101.
17. Resnick, S., 1987. Extreme Values, Regular Variation, and Point Processes. Springer, New York.
18. Robinson P.M. Nonparametric estimators for time series. J. Time Ser. Anal. 4:1983;81-101.
19. Roussas G.G. Nonparametric regression under mixing conditions. Stochastic Processes Appl. 36:1990;107-116.
20. Ruppert D., Wand M.P. Multivariate weighted least squares regression. Ann. Statist. 22:1994;107-116.
21. Taqqu M.S. Convergence of integrated processes of arbitrary Hermite rank. Z. Wahr- scheinlichkeitstheorie verw. Gebiete. 50:1979;53-83.
22. Truong Y.K., Stone C.J. Nonparametric estimation involving time series. Ann. Statist. 20:1992;77-97.