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Volumn 24, Issue 6, 1996, Pages 2608-2630

A general Bahadur representation of M-estimators and its application to linear regression with nonstochastic designs

Author keywords

Asymptotic approximation; Bahadur representation; Linear regression; M estimator; Minimum Lp distance estimators

Indexed keywords


EID: 0030343232     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032181172     Document Type: Article
Times cited : (198)

References (31)
  • 3
    • 0000318629 scopus 로고
    • Strong representation for LAD estimators in linear models
    • BABU, G. J. (1989). Strong representation for LAD estimators in linear models. Probab. Theory Related Fields 83 547-558.
    • (1989) Probab. Theory Related Fields , vol.83 , pp. 547-558
    • Babu, G.J.1
  • 4
    • 0000177625 scopus 로고
    • A note on quantiles in large samples
    • BAHADUR, R. R. (1966). A note on quantiles in large samples. Ann. Math. Statist. 37 577-581.
    • (1966) Ann. Math. Statist. , vol.37 , pp. 577-581
    • Bahadur, R.R.1
  • 5
    • 0000493352 scopus 로고
    • M-estimation of multivariate linear regression parameters under a convex discrepancy function
    • BAI, Z. D., RAO, C. R. and WU, Y. (1992). M-estimation of multivariate linear regression parameters under a convex discrepancy function. Statist. Sinica 2 237-254.
    • (1992) Statist. Sinica , vol.2 , pp. 237-254
    • Bai, Z.D.1    Rao, C.R.2    Wu, Y.3
  • 7
    • 0039196469 scopus 로고    scopus 로고
    • Bahadur representation of M-estimates based on U functionals
    • Dept. Statistics, Purdue Univ.
    • BOSE, A. (1996). Bahadur representation of M-estimates based on U functionals. Technical Report 96-2, Dept. Statistics, Purdue Univ.
    • (1996) Technical Report 96-2
    • Bose, A.1
  • 8
    • 0008222511 scopus 로고
    • On almost sure expansions for M-estimates
    • CARROLL, R. J. (1978). On almost sure expansions for M-estimates. Ann. Statist. 6 314-318.
    • (1978) Ann. Statist. , vol.6 , pp. 314-318
    • Carroll, R.J.1
  • 9
    • 0009206796 scopus 로고
    • On the law of the iterated logarithm for independent Banach space valued random variables
    • CHEN, X. (1993). On the law of the iterated logarithm for independent Banach space valued random variables. Ann. Probab. 21 1991-2011.
    • (1993) Ann. Probab. , vol.21 , pp. 1991-2011
    • Chen, X.1
  • 10
    • 0002384441 scopus 로고
    • On tail probability for martingales
    • FREEDMAN, D. (1975). On tail probability for martingales. Ann. Probab. 3 100-118.
    • (1975) Ann. Probab. , vol.3 , pp. 100-118
    • Freedman, D.1
  • 11
    • 0010774684 scopus 로고
    • Convexity and estimation
    • HABERMAN, S. J. (1989). Convexity and estimation. Ann. Statist. 17 1631-1661.
    • (1989) Ann. Statist. , vol.17 , pp. 1631-1661
    • Haberman, S.J.1
  • 13
    • 0039788837 scopus 로고
    • A strong Bahadur representation theorem of M-estimators
    • Dept. Mathematics, National Univ. Singapore
    • HE, X. and SHAQ, Q. M. (1994). A strong Bahadur representation theorem of M-estimators. Research Report 590, Dept. Mathematics, National Univ. Singapore.
    • (1994) Research Report 590
    • He, X.1    Shaq, Q.M.2
  • 14
    • 84966202120 scopus 로고
    • Law of the iterated logarithm and invariance principle for M-estimators
    • HE, X, and WANG, G. (1995). Law of the iterated logarithm and invariance principle for M-estimators. Proc: Amer. Math. Soc. 123 563-573.
    • (1995) Proc: Amer. Math. Soc. , vol.123 , pp. 563-573
    • He, X.1    Wang, G.2
  • 15
    • 21344480342 scopus 로고
    • Rank-based estimates in the linear model with high breakdown point
    • HÖSSJER, O. (1994). Rank-based estimates in the linear model with high breakdown point. J. Amer. Statist. Assoc. 89 149-158.
    • (1994) J. Amer. Statist. Assoc. , vol.89 , pp. 149-158
    • Hössjer, O.1
  • 16
    • 0000250624 scopus 로고
    • The behavior of maximum likelihood estimates under nonstandard conditions
    • Univ. California Press, Berkeley
    • HUBER, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. Proc. Fifth Berkeley Symp. Math. Statist. Probab. 1 221-233. Univ. California Press, Berkeley.
    • (1967) Proc. Fifth Berkeley Symp. Math. Statist. Probab. , vol.1 , pp. 221-233
    • Huber, P.J.1
  • 17
    • 0039166413 scopus 로고
    • Representation of M-estimators with the second-order asymptotic distribution
    • JUREČKOVÁ, J. (1985). Representation of M-estimators with the second-order asymptotic distribution. Statist. Decisions 3 263-276.
    • (1985) Statist. Decisions , vol.3 , pp. 263-276
    • Jurečková, J.1
  • 18
    • 0007059518 scopus 로고
    • A second-order asymptotic distributional representation of M-estimators with discontinuous score functions
    • JUREČKOVÁ, J. and SEN, P. K. (1987). A second-order asymptotic distributional representation of M-estimators with discontinuous score functions. Ann. Probab. 15 814-823.
    • (1987) Ann. Probab. , vol.15 , pp. 814-823
    • Jurečková, J.1    Sen, P.K.2
  • 19
    • 0001152423 scopus 로고
    • On Bahadur representation of sample quantiles
    • KIEFER, J. (1967). On Bahadur representation of sample quantiles. Ann. Math. Statist. 38 1323-1342.
    • (1967) Ann. Math. Statist. , vol.38 , pp. 1323-1342
    • Kiefer, J.1
  • 20
    • 0000273843 scopus 로고
    • Regression quantiles
    • KOENKER, R. and BASSETT, G. (1978). Regression quantiles. Econometrica 46 33-50.
    • (1978) Econometrica , vol.46 , pp. 33-50
    • Koenker, R.1    Bassett, G.2
  • 21
    • 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. J. Multivariate Anal. 50 93-114.
    • (1994) J. Multivariate Anal. , vol.50 , pp. 93-114
    • Liese, F.1    Vajda, I.2
  • 22
    • 0040975316 scopus 로고
    • Almost sure expansion for M-estimators and S-estimators in regression
    • Dept. Statistics, Univ. Illinois
    • MARTINSEK, A. (1989). Almost sure expansion for M-estimators and S-estimators in regression. Technical Report 25, Dept. Statistics, Univ. Illinois.
    • (1989) Technical Report 25
    • Martinsek, A.1
  • 23
    • 21144480023 scopus 로고
    • Asymptotics for M-estimators defined by convex minimization
    • NIEMIRO, W. (1992). Asymptotics for M-estimators defined by convex minimization. Ann. Statist. 20 1514-1533.
    • (1992) Ann. Statist. , vol.20 , pp. 1514-1533
    • Niemiro, W.1
  • 24
    • 84971936861 scopus 로고
    • Asymptotics for least absolute deviation regression estimators
    • POLLARD, D. (1991). Asymptotics for least absolute deviation regression estimators. Econometric Theory 7 186-199.
    • (1991) Econometric Theory , vol.7 , pp. 186-199
    • Pollard, D.1
  • 25
    • 0001449652 scopus 로고
    • Adaptive L-estimation for linear models
    • PORTNOY, S. and KOENKER, R. (1989). Adaptive L-estimation for linear models. Ann. Statist. 17 362-381.
    • (1989) Ann. Statist. , vol.17 , pp. 362-381
    • Portnoy, S.1    Koenker, R.2
  • 29
    • 0039520944 scopus 로고
    • On M-process and M-estimation
    • WELSH, A. (1989). On M-process and M-estimation. Ann. Statist. 17 337-362.
    • (1989) Ann. Statist. , vol.17 , pp. 337-362
    • Welsh, A.1
  • 30
    • 0040975310 scopus 로고
    • Sufficient moment and truncated moment conditions for the law of the iterated logarithm
    • WITTMANN, R. (1987). Sufficient moment and truncated moment conditions for the law of the iterated logarithm. Probab. Theory Related Fields 75 509-530.
    • (1987) Probab. Theory Related Fields , vol.75 , pp. 509-530
    • Wittmann, R.1
  • 31
    • 0000007831 scopus 로고
    • Asymptotic behavior of M-estimators for the linear model
    • YOHAI, V. J. and MARONNA, R. A (1979). Asymptotic behavior of M-estimators for the linear model. Ann. Statist. 7 258-268.
    • (1979) Ann. Statist. , vol.7 , pp. 258-268
    • Yohai, V.J.1    Maronna, R.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.