Subsampling continuous parameter random fields and a Bernstein inequality

Statistics

Volumn 33, Issue 4, 2000, Pages 367-392

  Bertail, Patrice ^a,d   Politis, Dimitris N ^b   Rhomari, Nourheddine ^c  

^a UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c FACULTÉ DES SCIENCES   (Morocco)

^d CEMAGREF   (France)

Author keywords

Bernstein inequality; Bootstrap; Continuous random fields; Edgeworth expansion; Generalized jackknife; Strong mixing

Indexed keywords

EID: 0346107470     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331880008802701     Document Type: Article

References (34)

1. Bennett, G. (1962) Probability inequalities for the sum of independent random variables. J. Amer. Statist. Assoc., 57, 33-45.
2. Berbee, H. C. P. (1979) Random walks with stationary increments and renewal theory. Math. Centre Tracts. Amsterdam.
3. Bertail, P. (1997) Second order properties of an extrapolated Bootstrap without replacement: the i.i.d. and the strong-mixing cases. Bernoulli, 3, 149-179.
4. Bertail, P., Politis, D. N. and Romano, J. P. (1999) On subsampling estimators with unknown rate of convergence. J. Amer. Stat. Assoc., 94.
5. Bertail, P. and Politis, D. N. (1998) Extrapolation of subsampling distribution estimators in the i.i.d and stronglt-cases, submitted Canad. Journ. Stat.
6. Bickel, P. J. and Yahav, J. A. (1988) Richardson extrapolation and the bootstrap. J. Amer. Stat. Assoc., 83, 387-393.
7. Blackman, R. B. and Tukey, J. W. (1959) The measurement of power spectra from the point of view of communication engineering, Dover, New York.
8. Booth, J. G. and Hall, P. (1993) An improvement of the jackknife distribution function estimator. Ann. Statist., 21, 1476-1485.
9. Bosq, D. (1993) Bernstein-type large deviations inequalities for partial sums of strong-mixing processes. Statistics, 24, 59-70.
10. Bosq, D. (1996) Nonparametric Statistics for Stochastic Processes: Estimation and Prediction. Lecture Notes in Statistics, 110, Springer Verlag, New-York.
11. Bradley, R. (1983) Approximation theorems for strongly mixing random variables. Michigan Math. J., 30, 69-81.
12. Bradley, R. (1986) Basic properties of strong-mixing conditions. In: Eberlein, E. and Taqqu, M. S. (Eds.), Dependence in Probability and Statistics, pp. 165-192, Birkhäuser.
13. Brillinger, D. R. (1975) Time series: data analysis and theory, Holt, Rinehart and Winston, New York.
14. Brockwell, P. J. (1994) On continuous-time threshold ARMA processes. J. Statist. Plan. Infer., 39, 291-303.
15. Brockwell, P. J. and Davis, R. A. (1991) Time series: theory and methods, Springer, New York.
16. Brockwell, P. J. and Williams, R. J. (1997) On the existence and application of continuous-time threshold autoregressions of order two to appear in Advances Appl. Prob.
17. Carlstein, E. (1986) The use of subseries values for estimating the variance of a general statistic from a stationary sequence. Ann. Statist., 14, 1171-1179.
18. Doukhan, P. (1994) Mixing: Properties and Examples. Lecture Notes in Statistics, p. 85, Springer Verlag, New-York.
19. Efron, B. (1979) Bootstrap methods: another look at the jackknife. Ann. Statist., 7, 1-26.
20. Freedman, D. (1984) On bootstrapping two stage least squares estimates in stationary linear models, Ann. Statist., 12, 827-842.
21. Gray, H., Schucany, W. and Watkins, T. (1972) The Generalized Jackknife Statistics. Marcel Dekker, New-York.
22. Grenander, U. and Rosenblatt, M. (1957) Statistical analysis of stationary time series. Wiley, New York.
23. Isaacson, E. and Keller, H. B. (1966) Analysis of Numerical Methods. John Wiley, New-York.
24. Ivanov, A. V. and Leonenko, N. N. (1989) Statistical analysis of random fields. Kluwer Academic Publishers.
25. Künsch, H. R. (1989) The jackknife and the bootstrap for general stationary observations. Ann. Statist., 17, 1217-1241.
26. Kutoyants, Yu. A. (1984) Parameter estimation for stochastic process. Heldermann Verlag, Berlin.
27. Leblanc, F. (1994) Estimation of Marginal Density of a Continuous Time Stochastic Process by Wavelets and Application to Diffusion Processes. CREST working paper no. 9456.
28. Liu, R. and Singh, K. (1992) Moving blocks jackknife and bootstrap capture weak dependence. In: Exploring the Limits of the Bootstrp. Eds. Le Page, R. and Billard, L., John Wiley, New York.
29. Politis, D. N. and Romano, J. P. (1994) Large sample confidence regions based on subsamples under minimal assumptions. Ann. Statist., 22, 2031-2050.
30. Prakasa Rao, B. L. S. (1983) Nonparametcic Functional Estimation. Academic Press, New York.
31. Rhomari, N. (1994) Filtrage non-paramétrique pour les processus non nécessairement markoviens. Ph.D. Thesis, Univ. Paris 6, Paris, France.
32. Rosenblatt, M. (1985) Stationary Sequences and Random Fields. Birkhäuser.
33. Shao, J. and Tu, D. (1995) The Jackknife and Bootstrap, Springer, New York.
34. Veretennikov, A. (1994) On large deviation for diffusion processes under minimal smoothness conditions. C. R. Acad. Sci. Paris, t. 319, Serie I, pp. 727-732.