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Volumn 53, Issue 4, 2001, Pages 691-707

Strong universal pointwise consistency of recursive regression estimates

Author keywords

Conditional expectations; Covering; Kernel estimates; Nonparametric regression estimation; Partitioning estimates; Recursive estimation; Semi recursive estimation; Strong laws of large numbers; Strong universal pointwise consistency; Truncation

Indexed keywords


EID: 6644223093     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014692616736     Document Type: Article
Times cited : (26)

References (31)
  • 1
    • 0011874897 scopus 로고
    • Nonparametric sequential estimation of a multiple regression function
    • Ahmad, I. A. and Lin, P.-E. (1976). Nonparametric sequential estimation of a multiple regression function, Bulletin of Mathematical Statistics, 17, 63-75.
    • (1976) Bulletin of Mathematical Statistics , vol.17 , pp. 63-75
    • Ahmad, I.A.1    Lin, P.-E.2
  • 2
    • 0008160357 scopus 로고    scopus 로고
    • Strong universal pointwise consistency of some regression function estimates
    • Algoet, P. and Györfi, L. (1999). Strong universal pointwise consistency of some regression function estimates, J. Multivariate Anal., 71, 125-144.
    • (1999) J. Multivariate Anal. , vol.71 , pp. 125-144
    • Algoet, P.1    Györfi, L.2
  • 3
    • 0001405597 scopus 로고
    • A covering lemma with applications to differentiability of measures and singular integral operators
    • de Guzmán, M. (1970). A covering lemma with applications to differentiability of measures and singular integral operators, Studia Math., 34, 299-317.
    • (1970) Studia Math. , vol.34 , pp. 299-317
    • Guzmán, M.1
  • 4
    • 0001244757 scopus 로고
    • On the almost everywhere convergence of nonparametric regression function estimates
    • Devroye, L. (1981). On the almost everywhere convergence of nonparametric regression function estimates, Ann. Statist., 9, 1310-1319.
    • (1981) Ann. Statist. , vol.9 , pp. 1310-1319
    • Devroye, L.1
  • 5
    • 0001844070 scopus 로고
    • 1 error of partitioning estimates of a regression function
    • (eds. F. Konecny, J. Mogyoródi, and W. Wertz), Akadémiai Kiadó, Budapest
    • 1 error of partitioning estimates of a regression function, Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics (eds. F. Konecny, J. Mogyoródi, and W. Wertz), 67-76, Akadémiai Kiadó, Budapest.
    • (1983) Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics , pp. 67-76
    • Devroye, L.1    Györfi, L.2
  • 7
    • 0000568602 scopus 로고
    • Distribution-free consistency results in nonparametric discrimination and regression function estimation
    • Devroye, L. and Wagner, T. J. (1980a). Distribution-free consistency results in nonparametric discrimination and regression function estimation, Ann. Statist., 8, 231-239.
    • (1980) Ann. Statist. , vol.8 , pp. 231-239
    • Devroye, L.1    Wagner, T.J.2
  • 8
    • 0002284573 scopus 로고
    • 1 convergence of kernel estimators of regression functions with applications in discrimination
    • 1 convergence of kernel estimators of regression functions with applications in discrimination, Z. Wahrsch. Verw. Gebiete, 51, 15-25.
    • (1980) Z. Wahrsch. Verw. Gebiete , vol.51 , pp. 15-25
    • Devroye, L.1    Wagner, T.J.2
  • 9
    • 84913246976 scopus 로고
    • Asymptotically optimal probabilistic algorithms for pattern recognition and identification
    • Ser. Monogr., No. 3
    • Greblicki, W. (1974). Asymptotically optimal probabilistic algorithms for pattern recognition and identification, Prace Nauk. Inst. Cybernet. Tech. Politech. Wroclaw., No. 18., Ser. Monogr., No. 3.
    • (1974) Prace Nauk. Inst. Cybernet. Tech. Politech. Wroclaw. , vol.18
    • Greblicki, W.1
  • 10
    • 51249178643 scopus 로고
    • Fourier and Hermite series estimates of regession functions
    • Greblicki, W. and Pawlak, M. (1985). Fourier and Hermite series estimates of regession functions, Ann. Inst. Statist. Math., 37, 443-454.
    • (1985) Ann. Inst. Statist. Math. , vol.37 , pp. 443-454
    • Greblicki, W.1    Pawlak, M.2
  • 11
    • 0003094495 scopus 로고
    • Necessary and sufficient consistency conditions for a recursive kernel regression estimate
    • Greblicki, W. and Pawlak, M. (1987). Necessary and sufficient consistency conditions for a recursive kernel regression estimate, J. Multivariate Anal., 23, 67-76.
    • (1987) J. Multivariate Anal. , vol.23 , pp. 67-76
    • Greblicki, W.1    Pawlak, M.2
  • 12
    • 0000289318 scopus 로고
    • Distribution-free poiritwise consistency of kernel regression estimate
    • Greblicki, W., Krzyżak, A. and Pawlak, M. (1984). Distribution-free poiritwise consistency of kernel regression estimate, Ann. Statist., 12, 1570-1575.
    • (1984) Ann. Statist. , vol.12 , pp. 1570-1575
    • Greblicki, W.1    Krzyzak, A.2    Pawlak, M.3
  • 13
    • 0002438218 scopus 로고
    • Universal consistencies of a regression estimate for unbounded regression functions, nonparametric functional estimation
    • (ed. G. Roussas), Kluwer, Dordrecht
    • Györfi, L. (1991). Universal consistencies of a regression estimate for unbounded regression functions, Nonparametric Functional Estimation (ed. G. Roussas), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 329-338, Kluwer, Dordrecht.
    • (1991) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , pp. 329-338
    • Györfi, L.1
  • 14
    • 0031574624 scopus 로고    scopus 로고
    • On the strong universal consistency of a recursive regression estimate by Pál Révész
    • Györfi, L. and Walk, H. (1997). On the strong universal consistency of a recursive regression estimate by Pál Révész, Statist. Probab. Lett., 31, 177-183.
    • (1997) Statist. Probab. Lett. , vol.31 , pp. 177-183
    • Györfi, L.1    Walk, H.2
  • 15
    • 85006556421 scopus 로고    scopus 로고
    • Weak and strong universal consistency of semi-recursive kernel and partitioning regression estimates
    • Györfi, L., Kohler, M. and Walk, H. (1998). Weak and strong universal consistency of semi-recursive kernel and partitioning regression estimates, Statist. Decisions, 16, 1-18.
    • (1998) Statist. Decisions , vol.16 , pp. 1-18
    • Györfi, L.1    Kohler, M.2    Walk, H.3
  • 17
    • 0009885648 scopus 로고    scopus 로고
    • On a universal strong law of large numbers for conditional expectations
    • Kozek, A. S., Leslie, J. R. and Schuster, E. F. (1998). On a universal strong law of large numbers for conditional expectations, Bernoulli, 4, 143-165.
    • (1998) Bernoulli , vol.4 , pp. 143-165
    • Kozek, A.S.1    Leslie, J.R.2    Schuster, E.F.3
  • 18
    • 0001235159 scopus 로고
    • Global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation
    • Krzyżak, A. (1992). Global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation, IEEE Trans. Inform. Theory, IT-38, 1323-1338.
    • (1992) IEEE Trans. Inform. Theory , vol.IT-38 , pp. 1323-1338
    • Krzyzak, A.1
  • 19
    • 0021190397 scopus 로고
    • Almost everywhere convergence of a recursive regression function estimate and classification
    • Krzyżak, A. and Pawlak, M. (1984). Almost everywhere convergence of a recursive regression function estimate and classification, IEEE Trans. Inform. Theory, IT-30, 91-93.
    • (1984) IEEE Trans. Inform. Theory , vol.IT-30 , pp. 91-93
    • Krzyzak, A.1    Pawlak, M.2
  • 21
    • 84969882200 scopus 로고
    • Springer, Berlin, Heidelberg, New York
    • Loève, M. (1977). Probability I, 4th ed., Springer, Berlin, Heidelberg, New York.
    • (1977) Probability I, 4th Ed.
    • Loève, M.1
  • 22
    • 0000570382 scopus 로고
    • On estimating regression
    • Nadaraya, E. A. (1964). On estimating regression, Theory Probab. Appl., 9, 141-142.
    • (1964) Theory Probab. Appl. , vol.9 , pp. 141-142
    • Nadaraya, E.A.1
  • 23
    • 0000618559 scopus 로고
    • Robbins-Monro procedure in a Hilbert space and its application in the theory of learning processes I
    • Révész, P. (1973). Robbins-Monro procedure in a Hilbert space and its application in the theory of learning processes I, Studia Sci. Math. Hungar., 8, 391-398.
    • (1973) Studia Sci. Math. Hungar. , vol.8 , pp. 391-398
    • Révész, P.1
  • 24
    • 0001293371 scopus 로고
    • Consistent window estimation in nonparametric regression
    • Spiegelman, C. and Sacks, J. (1980). Consistent window estimation in nonparametric regression, Ann. Statist., 8, 240-246.
    • (1980) Ann. Statist. , vol.8 , pp. 240-246
    • Spiegelman, C.1    Sacks, J.2
  • 25
    • 0000388992 scopus 로고
    • Consistent nonparametric regression
    • Stone, C. J. (1977). Consistent nonparametric regression, Ann. Statist., 5, 595-645.
    • (1977) Ann. Statist. , vol.5 , pp. 595-645
    • Stone, C.J.1
  • 26
    • 0001254834 scopus 로고
    • On almost sure convergence of conditional empirical distribution functions
    • Stute, W. (1986). On almost sure convergence of conditional empirical distribution functions, Ann. Probab., 14, 891-901.
    • (1986) Ann. Probab. , vol.14 , pp. 891-901
    • Stute, W.1
  • 27
    • 0012477457 scopus 로고    scopus 로고
    • Almost sure convergence properties of Nadaraya-Watson regression estimates
    • (S. Yakowitz memorial volume) (eds. M. Dror, P. L'Ecuyer and F. Szidarovszky), Kluwer, Dordrecht (to appear)
    • Walk, H. (2000). Almost sure convergence properties of Nadaraya-Watson regression estimates, Modeling Uncertainty: An Examination of its Theory, Methods and Applications (S. Yakowitz memorial volume) (eds. M. Dror, P. L'Ecuyer and F. Szidarovszky), Kluwer, Dordrecht (to appear).
    • (2000) Modeling Uncertainty: An Examination of Its Theory, Methods and Applications
    • Walk, H.1
  • 28
    • 0001762424 scopus 로고
    • Smooth regression analysis
    • Watson, G. S. (1964). Smooth regression analysis, Sankhyā Ser. A, 26, 359-372.
    • (1964) Sankhyā Ser. A , vol.26 , pp. 359-372
    • Watson, G.S.1
  • 31
    • 0002098808 scopus 로고
    • Sequential estimation of a continuous probability density function and mode
    • Yamato, H. (1971). Sequential estimation of a continuous probability density function and mode, Bulletin of Mathematical Statistics, 14, 1-12.
    • (1971) Bulletin of Mathematical Statistics , vol.14 , pp. 1-12
    • Yamato, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.