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Volumn 57, Issue 2, 2005, Pages 291-313

Strong convergence of estimators as εn-minimisers of optimisation problems

Author keywords

Epi convergence; M estimators; Stochastic optimisation; Strong convergence

Indexed keywords

OPTIMIZATION; RANDOM PROCESSES; REGRESSION ANALYSIS;

EID: 26244463393     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/BF02507027     Document Type: Article
Times cited : (27)

References (34)
  • 1
    • 0001646484 scopus 로고
    • Cox's regression model for counting processes: A large sample study
    • Andersen, P. K. and Gill, R. D. (1982). Cox's regression model for counting processes: A large sample study, The Annals of Statistics, 10, 1100-1120.
    • (1982) The Annals of Statistics , vol.10 , pp. 1100-1120
    • Andersen, P.K.1    Gill, R.D.2
  • 3
    • 0001100357 scopus 로고
    • Stability results for stochastic programs and sensors, allowing for discontinuous objective functions
    • Artstein, Z. and Wets, R. J.-B. (1994). Stability results for stochastic programs and sensors, allowing for discontinuous objective functions, SIAM Journal on Optimization, 4, 537-550.
    • (1994) SIAM Journal on Optimization , vol.4 , pp. 537-550
    • Artstein, Z.1    Wets, R.J.-B.2
  • 4
    • 0042708389 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for consistency of M-estimates in regression models with general errors
    • Berlinet, A., Liese, F. and Vajda, I. (2000). Necessary and sufficient conditions for consistency of M-estimates in regression models with general errors, Journal of Statistical Planning and Inference, 89(1-2), 243-267.
    • (2000) Journal of Statistical Planning and Inference , vol.89 , Issue.1-2 , pp. 243-267
    • Berlinet, A.1    Liese, F.2    Vajda, I.3
  • 5
    • 0000825215 scopus 로고
    • A general Akaike-type criterion for model selection in robust regression
    • Burman, P. and Nolan, D. (1995). A general Akaike-type criterion for model selection in robust regression, Biometrika, 82, 877-886.
    • (1995) Biometrika , vol.82 , pp. 877-886
    • Burman, P.1    Nolan, D.2
  • 6
    • 0042113388 scopus 로고    scopus 로고
    • Consistency of M-estimators and one-sided bracketing
    • Proceedings of the conference in Oberwolfach (eds. E. Eberlein et al.), Birkhäuser, Basel
    • Dudley, R. M. (1998). Consistency of M-estimators and one-sided bracketing, High Dimensional Probability, Proceedings of the conference in Oberwolfach (eds. E. Eberlein et al.), 33-58, Birkhäuser, Basel.
    • (1998) High Dimensional Probability , pp. 33-58
    • Dudley, R.M.1
  • 7
    • 0001421130 scopus 로고
    • Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems
    • Dupačová, J. and Wets, R. J.-B. (1988). Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems, The Annals of Statistics, 16, 1517-1549.
    • (1988) The Annals of Statistics , vol.16 , pp. 1517-1549
    • Dupačová, J.1    Wets, R.J.-B.2
  • 8
    • 21844523306 scopus 로고
    • On the asymptotics of constrained M-estimation
    • Geyer, C. J. (1994). On the asymptotics of constrained M-estimation, The Annals of Statistics, 22, 1993-2010.
    • (1994) The Annals of Statistics , vol.22 , pp. 1993-2010
    • Geyer, C.J.1
  • 9
    • 0030488332 scopus 로고    scopus 로고
    • Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator
    • Hess, C. (1996). Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator, The Annals of Statistics, 24, 1298-1315.
    • (1996) The Annals of Statistics , vol.24 , pp. 1298-1315
    • Hess, C.1
  • 10
    • 77950501160 scopus 로고
    • Optimum solution of a stochastic optimization problem with unknown parameters
    • Transactions of the 7th Prague conference, Prague 1974
    • Kaňková, V. (1978). Optimum solution of a stochastic optimization problem with unknown parameters, Information Theory, Statistical Decision Functions, Random Processes, Transactions of the 7th Prague conference, Vol. B, Prague 1974, 239-244.
    • (1978) Information Theory, Statistical Decision Functions, Random Processes , vol.B , pp. 239-244
    • Kaňková, V.1
  • 11
    • 0001659305 scopus 로고
    • Asymptotic theory for solutions in statistical estimation and stochastic programming
    • King, A. J. and Rockafellar, T. (1993). Asymptotic theory for solutions in statistical estimation and stochastic programming, Mathematics of Operations Research, 18, 148-162.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 148-162
    • King, A.J.1    Rockafellar, T.2
  • 13
    • 0037300588 scopus 로고    scopus 로고
    • Estimation in nonlinear autoregressive models
    • Liebscher, E. (2003). Estimation in nonlinear autoregressive models, Journal of Multivariate Analysis, 84, 247-261.
    • (2003) Journal of Multivariate Analysis , vol.84 , pp. 247-261
    • Liebscher, E.1
  • 14
    • 0002367401 scopus 로고
    • Consistency of M-estimates in general regression models
    • Liese, F. and Vajda, I. (1994). Consistency of M-estimates in general regression models, Journal of Multivariate Analysis, 50, 93-114.
    • (1994) Journal of Multivariate Analysis , vol.50 , pp. 93-114
    • Liese, F.1    Vajda, I.2
  • 15
    • 21844481339 scopus 로고
    • Necessary and sufficient conditions for consistency of generalized M-estimates
    • Liese, F. and Vajda, I. (1995). Necessary and sufficient conditions for consistency of generalized M-estimates, Metrika, 42, 291-324.
    • (1995) Metrika , vol.42 , pp. 291-324
    • Liese, F.1    Vajda, I.2
  • 17
    • 33644629081 scopus 로고
    • On the measurability and consistency of minimum contrast estimates
    • Pfanzagl, J. (1969). On the measurability and consistency of minimum contrast estimates, Metrika, 14, 249-272.
    • (1969) Metrika , vol.14 , pp. 249-272
    • Pfanzagl, J.1
  • 19
    • 77950497479 scopus 로고    scopus 로고
    • Stochastic optimization and statistical inference
    • eds. A. Ruszczinski and A. Shapiro
    • Pflug, G. Ch. (2003). Stochastic optimization and statistical inference, Handbooks in Operations Research and Management Science (eds. A. Ruszczinski and A. Shapiro), 10, 427-482.
    • (2003) Handbooks in Operations Research and Management Science , vol.10 , pp. 427-482
    • Pflug, G.Ch.1
  • 20
    • 84971851120 scopus 로고
    • Effects of model selection on inference
    • Pötscher, B. M. (1991). Effects of model selection on inference, Econometric Theory, 7, 163-185.
    • (1991) Econometric Theory , vol.7 , pp. 163-185
    • Pötscher, B.M.1
  • 22
    • 0000070978 scopus 로고
    • A strongly consistent procedure for model selection in a regression problem
    • Rao, C. R. and Wu, Y. (1989). A strongly consistent procedure for model selection in a regression problem, Biometrika, 76, 369-374.
    • (1989) Biometrika , vol.76 , pp. 369-374
    • Rao, C.R.1    Wu, Y.2
  • 23
    • 0023315165 scopus 로고
    • Local epi-continuity and local optimization
    • Robinson, S. M. (1987). Local epi-continuity and local optimization, Mathematical Programming, 37, 208-222.
    • (1987) Mathematical Programming , vol.37 , pp. 208-222
    • Robinson, S.M.1
  • 25
    • 0000428682 scopus 로고
    • On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima
    • Salinetti, G. and Wets, R. J.-B. (1986). On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima, Mathematics of Operations Research, 11, 385-419.
    • (1986) Mathematics of Operations Research , vol.11 , pp. 385-419
    • Salinetti, G.1    Wets, R.J.-B.2
  • 26
    • 0001239612 scopus 로고
    • Asymptotic properties of statistical estimators in stochastic programming
    • Shapiro, A. (1989). Asymptotic properties of statistical estimators in stochastic programming, The Annals of Statistics, 17, 841-858.
    • (1989) The Annals of Statistics , vol.17 , pp. 841-858
    • Shapiro, A.1
  • 27
    • 0001530774 scopus 로고
    • Asymptotic analysis of stochastic programs
    • Shapiro, A. (1991). Asymptotic analysis of stochastic programs, Annals of Operations Research, 30, 169-186.
    • (1991) Annals of Operations Research , vol.30 , pp. 169-186
    • Shapiro, A.1
  • 29
    • 0002886544 scopus 로고
    • A stochastic approach to stability in stochastic programming
    • Vogel, S. (1994). A stochastic approach to stability in stochastic programming, Journal of Computational and Applied Mathematics, 56, 65-96.
    • (1994) Journal of Computational and Applied Mathematics , vol.56 , pp. 65-96
    • Vogel, S.1
  • 30
    • 0037481088 scopus 로고    scopus 로고
    • On continuous convergence and epi-convergence of random functions. Part I: Theory and relations
    • Vogel, S. and Lachout, P. (2003a). On continuous convergence and epi-convergence of random functions. Part I: Theory and relations, Kybernetika, 39, 75-98.
    • (2003) Kybernetika , vol.39 , pp. 75-98
    • Vogel, S.1    Lachout, P.2
  • 31
    • 0038494985 scopus 로고    scopus 로고
    • On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications
    • Vogel, S. and Lachout, P. (2003b). On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications, Kybernetika, 39, 99-118.
    • (2003) Kybernetika , vol.39 , pp. 99-118
    • Vogel, S.1    Lachout, P.2
  • 32
    • 0000167944 scopus 로고
    • Note on the consistency of the maximum likelihood estimate
    • Wald, A. (1949). Note on the consistency of the maximum likelihood estimate, The Annals of Mathematical Statistics, 20, 595-601.
    • (1949) The Annals of Mathematical Statistics , vol.20 , pp. 595-601
    • Wald, A.1
  • 33
    • 0009343242 scopus 로고
    • M-estimators for censored data: Strong consistency
    • Wang, J.-L. (1995). M-estimators for censored data: Strong consistency, Scandinavian Journal of Statistics, 22, 197-205.
    • (1995) Scandinavian Journal of Statistics , vol.22 , pp. 197-205
    • Wang, J.-L.1
  • 34
    • 0000480451 scopus 로고
    • Asymptotic theory of nonlinear least squares estimation
    • Wu, C.-F. (1981). Asymptotic theory of nonlinear least squares estimation, The Annals of Statistics, 9, 501-513.
    • (1981) The Annals of Statistics , vol.9 , pp. 501-513
    • Wu, C.-F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.