Nonparametric inference for ergodic, stationary time series

Annals of Statistics

Volumn 24, Issue 1, 1996, Pages 370-379

  Morvai, Gusztáv ^a   Yakowitz, Sidney ^b   Györfi, László ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b University of Arizona   (United States)

Author keywords

Nonparametric regression; Stationary ergodic process; Universal prediction schemes

Indexed keywords

EID: 0030551977     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1033066215     Document Type: Article

References (21)

1. ALGOET, P. (1992). Universal schemes for prediction, gambling and portfolio selection. Ann. Probab. 20 901-941.
2. ASH, R. (1972). Real Analysis and Probability. Academic Press, New York.
3. AZUMA, K. (1967). Weighted sums of certain dependent random variables. Tōhoku Math. J. 37 357-367.
4. BAILEY, D. (1976). Sequential schemes for classifying and predicting ergodic processes. Ph.D. dissertation, Dept. Mathematics, Stanford Univ.
5. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
6. CASTELLANA, J. V. and LEADBETTER, M. R. (1986). On smoothed probability density estimation for stationary processes. Stochastic Process. Appl. 21 179-193.
7. COLLOMB, G. (1985). Nonparametric time series analysis and prediction: uniform almost sure convergence. Statistics 2 197-307.
8. COVER, T. (1975). Open problems in information theory. In Moscow Information Theory Workshop. IEEE Press, New York.
9. 1-View. Wiley, New York.
10. GRAY, R. (1988). Probability, Random Processes, and Ergodic Properties. Springer, New York.
11. GYÖRFI, L. (1981). Strong consistent density estimation from ergodic sample. J. Multivariate Anal. 11 81-84.
12. GYÖRFI, L., HAERDLE, W., SARDA, P. and VIEU, PH. (1989). Nonparametric Curve Estimation from Time Series. Springer, Berlin.
13. GYÖRFI, L. and LUGOSI, G. (1992). Kernel density estimation from ergodic sample is not universally consistent. Comput. Statist. Data Anal. 14 437-442.
14. 2 strong consistency of recursive kernel density estimation from time series. IEEE Trans. Inform. Theory 36 531-539.
15. MASRY, E. (1986). Recursive probability density estimation for weakly dependent stationary processes. IEEE Trans. Inform. Theory IT-32 249-254.
16. ORNSTEIN, D. (1978). Guessing the next output of a stationary process. Israel J. Math. 30 292-296.
17. ROSENBLATT, M. (1970). Density estimates and Markov sequences. In Nonparametric Techniques in Statistical Inference (M. Puri, ed.) 199-210. Cambridge Univ. Press.
18. ROUSSAS, G. (1969). Non-parametric estimation of the transition distribution of a Markov process. Ann. Inst. Statist. Math. 21 73-87.
19. STOUT, W. F. (1974). Almost Sure Convergence. Academic Press, New York.
20. YAKOWITZ, S. (1989). Nonparametric density and regression estimation for Markov sequences without mixing assumptions. J. Multivariate Anal. 30 124-136.
21. YAKOWITZ, S. (1993). Nearest neighbor regression estimation for null-recurrent Markov time series. Stochastic Process. Appl. 37 311-318.