메뉴 건너뛰기




Volumn 67, Issue 1, 1999, Pages 1-14

Uniform consistency of the partitioning estimate under ergodic conditions

Author keywords

Autoregression; Ergodic processes; Martingale difference; Partitioning estimate; Prediction; Regression; Stationarity

Indexed keywords


EID: 0040708924     PISSN: 14467887     EISSN: None     Source Type: Journal    
DOI: 10.1017/s1446788700000835     Document Type: Article
Times cited : (3)

References (34)
  • 1
    • 0000115649 scopus 로고
    • Non-strong mixing autoregressive processes
    • D. W. K. Andrews, 'Non-strong mixing autoregressive processes', J. Appl. Probab. 21 (1984), 930-934.
    • (1984) J. Appl. Probab. , vol.21 , pp. 930-934
    • Andrews, D.W.K.1
  • 3
    • 0010098468 scopus 로고
    • Nonparametric prediction for unbounded almost stationary processes
    • Kluwer Acad. Publ., Amsterdam
    • D. Bosq, 'Nonparametric prediction for unbounded almost stationary processes', in: Nonparametric functional estimation and related topics (Kluwer Acad. Publ., Amsterdam, 1991) pp. 389-403.
    • (1991) Nonparametric Functional Estimation and Related Topics , pp. 389-403
    • Bosq, D.1
  • 4
    • 0004256573 scopus 로고
    • Addison-Wesley, Reading, MA
    • L. Breiman, Probability (Addison-Wesley, Reading, MA, 1968).
    • (1968) Probability
    • Breiman, L.1
  • 5
    • 84946380048 scopus 로고
    • Partitioning estimates of regression function under random censoring
    • A. Carbonez, L. Györfi and E. C. Van der Meulen, 'Partitioning estimates of regression function under random censoring', Statist. Decisions 13 (1995), 21-37.
    • (1995) Statist. Decisions , vol.13 , pp. 21-37
    • Carbonez, A.1    Györfi, L.2    Van Der Meulen, E.C.3
  • 6
    • 0001908707 scopus 로고
    • Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations
    • G. Collomb and W. Härdle, 'Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations', Stochastic Process. Appl. 23 (1986), 77-89.
    • (1986) Stochastic Process. Appl. , vol.23 , pp. 77-89
    • Collomb, G.1    Härdle, W.2
  • 7
    • 0039090902 scopus 로고
    • Sur l'estimationn de la densité pour des observations ergodiques
    • M. Delecroix, M. N. Nogueira and A. C. Martins Rosa, 'Sur l'estimationn de la densité pour des observations ergodiques', Stat. et Anal des données 16 (1991), 25-38.
    • (1991) Stat. et Anal des Données , vol.16 , pp. 25-38
    • Delecroix, M.1    Nogueira, M.N.2    Rosa, A.C.M.3
  • 8
    • 0001580091 scopus 로고    scopus 로고
    • Nonparametric estimation of a regression function and its derivatives under an ergodic hypothesis
    • M. Delecroix and A. C. Rosa, 'Nonparametric estimation of a regression function and its derivatives under an ergodic hypothesis', J. Nonparametric Statistics 6 (1996), 367-382.
    • (1996) J. Nonparametric Statistics , vol.6 , pp. 367-382
    • Delecroix, M.1    Rosa, A.C.2
  • 10
    • 46049096298 scopus 로고
    • A weak invariance principle for cumulated functional of the regressogram estimator with dependent data
    • J. Diebolt and N. Laïb, 'A weak invariance principle for cumulated functional of the regressogram estimator with dependent data', J. Nonparametr. Statist. 4 (1994), 149-163.
    • (1994) J. Nonparametr. Statist. , vol.4 , pp. 149-163
    • Diebolt, J.1    Laïb, N.2
  • 11
    • 0005846282 scopus 로고
    • Consistent nonparametric regression from recursive partitioning schemes
    • L. Gordon and R. A. Olshen, 'Consistent nonparametric regression from recursive partitioning schemes', J. Multivariate Anal. 10 (1980), 611-627.
    • (1980) J. Multivariate Anal. , vol.10 , pp. 611-627
    • Gordon, L.1    Olshen, R.A.2
  • 12
    • 0001743179 scopus 로고
    • Almost sure consistent nonparametric regression from recursive partitioning schemes
    • _, 'Almost sure consistent nonparametric regression from recursive partitioning schemes', J. Multivariate Anal. 15 (1984), 147-163.
    • (1984) J. Multivariate Anal. , vol.15 , pp. 147-163
  • 13
    • 0001839725 scopus 로고
    • Strong consistent density estimate from ergodic sample
    • L. Györfi, 'Strong consistent density estimate from ergodic sample', J. Multivariate Anal. 11 (1981), 81-84.
    • (1981) J. Multivariate Anal. , vol.11 , pp. 81-84
    • Györfi, L.1
  • 14
    • 0002438218 scopus 로고
    • Universal consistencies of a regression estimate for unbounded regression function
    • (ed. Roussas) Kluwer Acad. Publ., Amsterdam
    • _, 'Universal consistencies of a regression estimate for unbounded regression function', in: Nonparametric functional estimation and related topics (ed. Roussas) (Kluwer Acad. Publ., Amsterdam, 1991) pp. 329-338.
    • (1991) Nonparametric Functional Estimation and Related Topics , pp. 329-338
  • 16
    • 38249010056 scopus 로고
    • Kernel density estimation from ergodic sample is not universally consistent
    • L. Györfi and G. Lugosi, 'Kernel density estimation from ergodic sample is not universally consistent', Comput. Statist. Data Anal. 14 (1992), 437-442.
    • (1992) Comput. Statist. Data Anal. , vol.14 , pp. 437-442
    • Györfi, L.1    Lugosi, G.2
  • 17
    • 0025434760 scopus 로고
    • 2 strong consistency of recursive kernel density estimation from dependent samples
    • 2 strong consistency of recursive kernel density estimation from dependent samples', IEEE Trans. Inform. Theory 36 (1990), 531-539.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 531-539
    • Györfi, L.1    Masry, E.2
  • 18
    • 0032027780 scopus 로고    scopus 로고
    • Limits to consistent on line forecasting for ergodic time series
    • L. Györfi, G. Morvai and S. Yakowitz, 'Limits to consistent on line forecasting for ergodic time series', IEEE Trans. Inform. Theory 44 (1998), 868-892.
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 868-892
    • Györfi, L.1    Morvai, G.2    Yakowitz, S.3
  • 19
    • 0000272104 scopus 로고
    • Data driven bandwidth choice for density estimation based on dependent data
    • J. Hart and P. Vieu, 'Data driven bandwidth choice for density estimation based on dependent data', Ann. Statist. 18 (1990), 837-890.
    • (1990) Ann. Statist. , vol.18 , pp. 837-890
    • Hart, J.1    Vieu, P.2
  • 21
    • 33749118637 scopus 로고    scopus 로고
    • Exponential-type inequalities for martingale difference sequences. Application to nonparametric regression estimation
    • to appear
    • N. Laïb, 'Exponential-type inequalities for martingale difference sequences. Application to nonparametric regression estimation', Comm. Statist. Theory Methods, to appear.
    • Comm. Statist. Theory Methods
    • Laïb, N.1
  • 22
    • 0039039076 scopus 로고
    • Estimation non-paramétrique de la régression pour des données dépendantes. Application à la prévision
    • _, 'Estimation non-paramétrique de la régression pour des données dépendantes. Application à la prévision', C. R. Acad. Sci. Paris 317 (1993), 1173-1177.
    • (1993) C. R. Acad. Sci. Paris , vol.317 , pp. 1173-1177
  • 23
    • 4243815757 scopus 로고    scopus 로고
    • Estimation non-paramétrique robuste de la fonction de régression pour des observations ergodiques
    • N. Laïb and E. Ould-Saïd, 'Estimation non-paramétrique robuste de la fonction de régression pour des observations ergodiques', C. R. Acad. Sci. Paris 320 (1996), 271-276.
    • (1996) C. R. Acad. Sci. Paris , vol.320 , pp. 271-276
    • Laïb, N.1    Ould-Saïd, E.2
  • 24
    • 0001194690 scopus 로고
    • Weak and strong uniform consistency of kernel regression estimates
    • Y. P. Mack and B. W. Silverman, 'Weak and strong uniform consistency of kernel regression estimates', Z. Wahrsch. Verw. Gebiete 61 (1982), 405-415.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.61 , pp. 405-415
    • Mack, Y.P.1    Silverman, B.W.2
  • 25
    • 0040151548 scopus 로고    scopus 로고
    • A note on ergodic processes prediction via estimation of the conditional mode function
    • E. Ould-Saïd, 'A note on ergodic processes prediction via estimation of the conditional mode function', Scand. J. Statist. 2 (1997), 231-240.
    • (1997) Scand. J. Statist. , vol.2 , pp. 231-240
    • Ould-Saïd, E.1
  • 26
    • 0001155464 scopus 로고
    • Some mixing properties of time series models
    • T. D. Pham and T. Tran, 'Some mixing properties of time series models', Stochastic Process. Appl. 19 (1985), 279-303.
    • (1985) Stochastic Process. Appl. , vol.19 , pp. 279-303
    • Pham, T.D.1    Tran, T.2
  • 27
    • 0039683139 scopus 로고
    • Estimation non-paramétrique de la médianne conditionnelle sous hypothèse ergodique. Application à la prévision des processus
    • Bruxelles
    • e Journées de statistiques,' Bruxelles, (1992) pp. 325-328.
    • (1992) e Journées de Statistiques , pp. 325-328
    • Rosa, A.C.1
  • 28
    • 0040274914 scopus 로고
    • Dependence and asymptotic independence from random processes
    • M. Rosenblatt, 'Dependence and asymptotic independence from random processes', M.A.A. Stud. Math. 18 (1978), 24-45.
    • (1978) M.A.A. Stud. Math. , vol.18 , pp. 24-45
    • Rosenblatt, M.1
  • 29
    • 0002591194 scopus 로고
    • Nonparametric regression estimation under mixing conditions
    • G. G. Roussas, 'Nonparametric regression estimation under mixing conditions', Stochastic Process. Appl. 36 (1990), 107-116.
    • (1990) Stochastic Process. Appl. , vol.36 , pp. 107-116
    • Roussas, G.G.1
  • 30
    • 0010888380 scopus 로고
    • L. T. Tran, 'nonparametric function estimation for time series by local average estimators'
    • L. T. Tran, 'Nonparametric function estimation for time series by local average estimators', Ann. Statist. 21 (1993), 1040-1057.
    • (1993) Ann. Statist. , vol.21 , pp. 1040-1057
  • 31
    • 0002636269 scopus 로고
    • Robust nonparametric regression in time series
    • Y. K. Truong, 'Robust nonparametric regression in time series', J. Multivariate Anal. 41 (1992), 163-177.
    • (1992) J. Multivariate Anal. , vol.41 , pp. 163-177
    • Truong, Y.K.1
  • 32
    • 0001917688 scopus 로고
    • Nonparametric function estimation involving time series
    • Y. K. Truong and C. J. Stone, 'Nonparametric function estimation involving time series', Ann. Statist. 20 (1992), 77-97.
    • (1992) Ann. Statist. , vol.20 , pp. 77-97
    • Truong, Y.K.1    Stone, C.J.2
  • 33
    • 0001646148 scopus 로고
    • Central limit theorems for dependent variables
    • C. S. Withers, 'Central limit theorems for dependent variables', Z. Wahrsch. Verw. Gebiete 57 (1981b), 509-534.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.57 , pp. 509-534
    • Withers, C.S.1
  • 34
    • 38249021954 scopus 로고
    • Nonparametric density and regression estimation for Markov sequences without mixing assumptions
    • S. Yakowitz, 'Nonparametric density and regression estimation for Markov sequences without mixing assumptions', J. Multivariate Anal. 30 (1989), 124-136.
    • (1989) J. Multivariate Anal. , vol.30 , pp. 124-136
    • Yakowitz, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.