메뉴 건너뛰기




Volumn 84, Issue 2, 2003, Pages 247-261

Strong convergence of estimators in nonlinear autoregressive models

Author keywords

M estimators; Nonlinear autoregressive model; Strong convergence; Threshold models

Indexed keywords


EID: 0037300588     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(02)00022-2     Document Type: Review
Times cited : (9)

References (38)
  • 1
    • 0000482273 scopus 로고
    • Criteria of ergodicity for some models with a markovian representation
    • (in French)
    • P. Ango Nze, Criteria of ergodicity for some models with a markovian representation (in French), C. R. Acad. Sci. Paris Sér. I t. 315 (1992) 1301-1304.
    • (1992) C. R. Acad. Sci. Paris Sér. I T. , vol.315 , pp. 1301-1304
    • Ango Nze, P.1
  • 2
    • 0012534920 scopus 로고
    • Some strong limit theorems for M-estimators
    • M.A. Arcones, Some strong limit theorems for M-estimators, Stochastic Process. Appl. 53 (1994) 241-268.
    • (1994) Stochastic Process. Appl. , vol.53 , pp. 241-268
    • Arcones, M.A.1
  • 3
    • 0001634017 scopus 로고
    • General M-estimates for contaminated pth-order autoregressive processes: Consistency and asymptotic normality. Robustness in autoregressive processes
    • O.H. Bustos, General M-estimates for contaminated pth-order autoregressive processes: consistency and asymptotic normality. Robustness in autoregressive processes, Z. Wahrsch. Verw. Gebiete 59 (1982) 491-504.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.59 , pp. 491-504
    • Bustos, O.H.1
  • 4
    • 21144465257 scopus 로고
    • Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model
    • K.S. Chan, Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model, Ann. Statist. 21 (1993) 520-533.
    • (1993) Ann. Statist. , vol.21 , pp. 520-533
    • Chan, K.S.1
  • 6
    • 84986792427 scopus 로고
    • On estimating thresholds in autoregressive models
    • K.S. Chan, H. Tong, On estimating thresholds in autoregressive models, J. Time Ser. Anal. 7 (1986) 179-190.
    • (1986) J. Time Ser. Anal. , vol.7 , pp. 179-190
    • Chan, K.S.1    Tong, H.2
  • 7
    • 0003155075 scopus 로고
    • Mixing: Properties and Examples
    • Springer, Berlin
    • P. Doukhan, Mixing: Properties and Examples, Lecture Notes in Statistics, Vol. 85, Springer, Berlin, 1994.
    • (1994) Lecture Notes in Statistics , vol.85
    • Doukhan, P.1
  • 8
    • 0032063592 scopus 로고    scopus 로고
    • Estimating linear representations of nonlinear processes
    • C. Francq, J.-M. Zakoïan, Estimating linear representations of nonlinear processes, J. Statist. Plann. Inference 68 (1998) 145-165.
    • (1998) J. Statist. Plann. Inference , vol.68 , pp. 145-165
    • Francq, C.1    Zakoïan, J.-M.2
  • 13
    • 0012535698 scopus 로고
    • Large sample inference based on multiple observations from nonlinear autoregressive processes
    • S.Y. Hwang, I.V. Basawa, Large sample inference based on multiple observations from nonlinear autoregressive processes, Stochastic Process. Appl. 49 (1994) 127-140.
    • (1994) Stochastic Process. Appl. , vol.49 , pp. 127-140
    • Hwang, S.Y.1    Basawa, I.V.2
  • 14
    • 0000091003 scopus 로고
    • Asymptotic properties of non-linear least squares estimators
    • R.I. Jennrich, Asymptotic properties of non-linear least squares estimators, Ann. Math. Statist. 40 (1969) 633-643.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 633-643
    • Jennrich, R.I.1
  • 15
    • 0000471755 scopus 로고
    • On conditional least-squares estimation for stochastic processes
    • L.A. Klimko, P.L. Nelson, On conditional least-squares estimation for stochastic processes, Ann. Statist. 6 (1978) 629-642.
    • (1978) Ann. Statist. , vol.6 , pp. 629-642
    • Klimko, L.A.1    Nelson, P.L.2
  • 16
    • 0030546333 scopus 로고    scopus 로고
    • Asymptotics of some estimators and sequential residual empiricals in non-linear time series
    • H.L. Koul, Asymptotics of some estimators and sequential residual empiricals in non-linear time series, Ann. Statist. 24 (1996) 380-404.
    • (1996) Ann. Statist. , vol.24 , pp. 380-404
    • Koul, H.L.1
  • 17
    • 0000212399 scopus 로고
    • Bahadur-Kiefer representations for GM-estimators in autoregression models
    • H.L. Koul, Z. Zhu, Bahadur-Kiefer representations for GM-estimators in autoregression models, Stochastic Process. Appl. 57 (1995) 167-189.
    • (1995) Stochastic Process. Appl. , vol.57 , pp. 167-189
    • Koul, H.L.1    Zhu, Z.2
  • 18
    • 21844490193 scopus 로고
    • Asymptotic properties of nonlinear least squares estimates in stochastic regression models
    • T.L. Lai, Asymptotic properties of nonlinear least squares estimates in stochastic regression models, Ann. Statist. 22 (1994) 1917-1930.
    • (1994) Ann. Statist. , vol.22 , pp. 1917-1930
    • Lai, T.L.1
  • 19
    • 0030582828 scopus 로고    scopus 로고
    • Strong convergence of sums of α-mixing random variables with applications to density estimation
    • E. Liebscher, Strong convergence of sums of α-mixing random variables with applications to density estimation, Stochastic Process. Appl. 65 (1996) 69-80.
    • (1996) Stochastic Process. Appl. , vol.65 , pp. 69-80
    • Liebscher, E.1
  • 20
    • 85014758967 scopus 로고    scopus 로고
    • Estimation of the density and the regression function under mixing conditions
    • E. Liebscher, Estimation of the density and the regression function under mixing conditions, Statist. Decisions 19 (2001) 9-26.
    • (2001) Statist. Decisions , vol.19 , pp. 9-26
    • Liebscher, E.1
  • 21
    • 0002367401 scopus 로고
    • Consistency of M-estimates in general regression models
    • F. Liese, I. Vajda, Consistency of M-estimates in general regression models, J. Multivariate Anal. 50 (1994) 93-114.
    • (1994) J. Multivariate Anal. , vol.50 , pp. 93-114
    • Liese, F.1    Vajda, I.2
  • 22
    • 0000441740 scopus 로고
    • The consistency of nonlinear regression
    • E. Malinvaud, The consistency of nonlinear regression, Ann. Math. Statist. 41 (1970) 956-969.
    • (1970) Ann. Math. Statist. , vol.41 , pp. 956-969
    • Malinvaud, E.1
  • 23
    • 84974185463 scopus 로고
    • Nonparametric estimation and identification of nonlinear ARCH time series
    • E. Masry, D. Tjøstheim, Nonparametric estimation and identification of nonlinear ARCH time series, Econometric Theory 11 (1995) 258-289.
    • (1995) Econometric Theory , vol.11 , pp. 258-289
    • Masry, E.1    Tjøstheim, D.2
  • 24
    • 84986743964 scopus 로고
    • On the consistency of least squares estimator of a threshold AR(1) model
    • J.D. Petruccelli, On the consistency of least squares estimator of a threshold AR(1) model, J. Time Ser. Anal. 7 (1986) 269-278.
    • (1986) J. Time Ser. Anal. , vol.7 , pp. 269-278
    • Petruccelli, J.D.1
  • 25
    • 0000502581 scopus 로고
    • Strong consistency of the least squares estimator for a non-ergodic threshold autoregressive model
    • D.T. Pham, K.S. Chan, H. Tong, Strong consistency of the least squares estimator for a non-ergodic threshold autoregressive model, Statistica Sinica 1 (1991) 361-369.
    • (1991) Statistica Sinica , vol.1 , pp. 361-369
    • Pham, D.T.1    Chan, K.S.2    Tong, H.3
  • 26
    • 38249040640 scopus 로고
    • A class of partially adaptive one-step M-estimators for a nonlinear regression model with dependent observations
    • B.M. Pötscher, I.R. Prucha, A class of partially adaptive one-step M-estimators for a nonlinear regression model with dependent observations, J. Econometrics 32 (1986) 219-225.
    • (1986) J. Econometrics , vol.32 , pp. 219-225
    • Pötscher, B.M.1    Prucha, I.R.2
  • 29
    • 0001676485 scopus 로고
    • Consistent estimators in nonlinear regression for a noncompact parameter space
    • G.D. Richardson, B.B. Bhattacharyya, Consistent estimators in nonlinear regression for a noncompact parameter space, Ann. Statist. 14 (1986) 1591-1596.
    • (1986) Ann. Statist. , vol.14 , pp. 1591-1596
    • Richardson, G.D.1    Bhattacharyya, B.B.2
  • 30
    • 0001507728 scopus 로고
    • The functional law of the iterated logarithm for stationary strongly mixing sequences
    • E. Rio, The functional law of the iterated logarithm for stationary strongly mixing sequences, Ann. Statist. 23 (1995) 1188-1203.
    • (1995) Ann. Statist. , vol.23 , pp. 1188-1203
    • Rio, E.1
  • 31
    • 0001530774 scopus 로고
    • Asymptotic analysis of stochastic programs
    • A. Shapiro, Asymptotic analysis of stochastic programs, Ann. Oper. Res. 30 (1991) 169-186.
    • (1991) Ann. Oper. Res. , vol.30 , pp. 169-186
    • Shapiro, A.1
  • 32
    • 0028527813 scopus 로고
    • Quantitative stability in stochastic programming
    • A. Shapiro, Quantitative stability in stochastic programming, Math. Programming 67 (1994) 99-108.
    • (1994) Math. Programming , vol.67 , pp. 99-108
    • Shapiro, A.1
  • 33
    • 46149141205 scopus 로고
    • Estimation in nonlinear time series models
    • D. Tjøstheim, Estimation in nonlinear time series models, Stochastic Process. Appl. 21 (1986) 251-273.
    • (1986) Stochastic Process. Appl. , vol.21 , pp. 251-273
    • Tjøstheim, D.1
  • 34
    • 0001590528 scopus 로고
    • Non-linear time series and Markov chains
    • D. Tjøstheim, Non-linear time series and Markov chains, Adv. Appl. Probab. A 22 (1990) 587-611.
    • (1990) Adv. Appl. Probab. A , vol.22 , pp. 587-611
    • Tjøstheim, D.1
  • 37
    • 0000480451 scopus 로고
    • Asymptotic theory of nonlinear least squares estimation
    • C.-F. Wu, Asymptotic theory of nonlinear least squares estimation, Ann. Statist. 9 (1981) 501-513.
    • (1981) Ann. Statist. , vol.9 , pp. 501-513
    • Wu, C.-F.1
  • 38
    • 0000007831 scopus 로고
    • Asymptotic behavior of M-estimators for the linear model
    • V.J. Yohai, R.A. Maronna, Asymptotic behavior of M-estimators for the linear model, Ann. Statist. 7 (1979) 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.