Limits to classification and regression estimation from ergodic processes

Annals of Statistics

Volumn 27, Issue 1, 1999, Pages 262-273

  Nobel, Andrew B ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

Classification; Counterexamples; Ergodic processes; Reduction arguments; Regression

Indexed keywords

EID: 0033243867     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1018031110     Document Type: Article

References (33)

1. ADAMS, T. M. (1997). Families of ergodic processes without consistent density or regression estimates. Preprint.
2. ADAMS, T. M. and NOBEL, A. B. (1998). On density estimation from ergodic processes. Ann. Probab. 26 794-804.
3. ALGOET, P. (1992). Universal schemes for prediction, gambling and portfolio selection. Ann. Probab. 20 901-941. Correction: [Ann. Probab. 23 474-478 (1995).]
4. ASH, R. (1972). Real Analysis and Probability. Academic Press, New York.
5. BAILEY, D. H. (1976). Sequential schemes for classifying and predicting ergodic processes. Ph.D. dissertation, Dept. Mathematics, Stanford Univ.
6. BARRON, A. R. (1985). Logically smooth density estimation. Technical Report TR 56, Dept. Statistics, Stanford Univ.
7. CHENG, B. C. and ROBINSON, P. M. (1991). Density estimation in strongly dependent non-linear time series. Statist. Sinica 1 335-359.
8. DELECROIX, M. (1987). Sur l'estimation et la prévision non-paramétrique des processus ergodiques. Ph.D. thesis, Univ. Lille Flandres Artois, Lille, France.
9. DELECROIX, M. and ROSA, A. C. (1996). Nonparametric estimation of a regression function and its derivatives under an ergodic hypothesis. J. Nonparametric Statist. 6 367-382.
10. DEVROYE, L. and WAGNER, T. (1980). Distribution-free consistency results in nonparametric discrimination and regression function estimation. Ann. Statist. 8 231-239.
11. DEVROYE, L., GYÖRFI, L. and LUGOSI, G. (1996). A Probabalistic Theory of Pattern Recognition. Springer, New York.
12. GYÖRFI, L. (1981). Strongly consistent density estimate from ergodic sample. J. Multivariate Anal. 11 81-84.
13. GYÖRFI, L., HäRDLE, W., SARDA, P. and VIEU. P. (1989). Nonparametric Curve Estimation from Time Series. Springer, Berlin.
14. GYÖRFI, L. and LUGOSI, G. (1992). Kernel density estimation from ergodic sample is not universally consistent. Comput. Statist. Data Anal. 14 437-442.
15. GYÖRFI, L., MORVAI, G. and YAKOWITZ, S. (1998). Limits to consistent on-line forecasting for ergodic time series. IEEE Trans. Inform. Theory 44 886-892.
16. HIDALGO, J. (1997). Non-parametric estimation with strongly dependent time multivariate time series. J. Time Ser. Anal. 18 95-122.
17. Ho, H. C. (1995). On the strong uniform consistency of density estimation for strongly dependent sequences. Statist. Probab. Lett. 22 149-156.
18. MASRY, E. (1996). Multivariate local polynomial regression for time series: uniform strong consistency and rates. J. Time Ser. Anal. 17 571-599.
19. MORVAI, G., YAKOWITZ, S. and ALGOET, P. (1997). Weakly convergent nonparametric forecasting of stationary time series. IEEE Trans. Inform. Theory 43 483-498.
20. MORVAI, G., YAKOWITZ, S. and GYÖRFI, L. (1996). Nonparametric inference for ergodic, stationary time series. Ann. Statist. 24 370-379.
21. MORVAI, G., KULKARNI, S. and NOBEL, A. B. (1997). Regression estimation from an individual stationary sequence. Unpublished manuscript.
22. NOBEL, A. B., MORVAI, G. and KULKARNI, S. (1997). Density estimation from an individual numerical sequence. IEEE Trans. Inform. Theory 44 537-541.
23. ORNSTEIN, D. S. (1978). Guessing the next output of a stationary process. Israel J. Math. 30 292-296.
24. ROSENBLATT, M. (1970). Density estimates and Markov sequences. In Nonparametric Techniques in Statistical Inference (M. Puri, ed.) 199-210. Cambridge Univ. Press, London.
25. ROSENBLATT, M. (1991). Stochastic Curve Estimation. IMS, Hayward, CA.
26. ROUSSAS, G. (1967). Nonparametric estimation in Markov processes. Ann. Inst. Statist. Math. 21 73-87.
27. ROUSSAS, G. (1969). Nonparametric estimation of the transition distribution function of a Markov process. Ann. Math. Statist. 40 1386-1400.
28. RYABKO, B. YA. (1988). Prediction of random sequences and universal coding. Problems Inform. Transmission 24 87-96.
29. SPIEGELMAN, C. and SACKS, J. (1980). Consistent window estimation in nonparametric regression. Ann. Statist. 8 240-246.
30. STONE, C. (1977). Consistent nonparametric regression. Ann. Statist. 5 595-620.
31. YAKOWITZ, S. (1993). Nearest neighbor regression estimation for null-recurrent Markov time series. Stochastic Process. Appl. 48 311-318.
32. YAKOWITZ, S., GYÖRFI, L., KIEFFER, J. and MORVAI, G. (1997). Strongly consistent nonparametric estimation of smooth regression functions for stationary ergodic sequences. J. Multivariate Anal. To appear.
33. YAKOWITZ, S. and HEYDE, C. (1997). Long range dependency effects with implications for forecasting and queueing inference. Unpublished manuscript.