메뉴 건너뛰기




Volumn 37, Issue 1, 2009, Pages 223-245

Monte Carlo maximum likelihood estimation for discretely observed diffusion processes

Author keywords

Coupling; Exact simulation; Linear diffusion processes; Random function; SLLN on Banach space; Uniform convergence

Indexed keywords


EID: 65349123487     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOS550     Document Type: Article
Times cited : (67)

References (40)
  • 1
    • 0036216388 scopus 로고    scopus 로고
    • Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach
    • MR1926260
    • AÏT-SAHALIA, Y. (2002). Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach. Econometrica 70 223-262. MR1926260
    • (2002) Econometrica , vol.70 , pp. 223-262
    • AÏT-SAHALIA, Y.1
  • 2
    • 0001761552 scopus 로고
    • Consistency in nonlinear econometric models: A generic uniform law of large numbers
    • MR0923471
    • ANDREWS, D. W. K. (1987). Consistency in nonlinear econometric models: A generic uniform law of large numbers. Econometrica 55 1465-1471. MR0923471
    • (1987) Econometrica , vol.55 , pp. 1465-1471
    • ANDREWS, D.W.K.1
  • 3
    • 21344441885 scopus 로고
    • Discretization error in simulation of onedimensional reflecting Brownian motion
    • MR1384357
    • ASMUSSEN, S., GLYNN, P. and PITMAN, J. (1995). Discretization error in simulation of onedimensional reflecting Brownian motion. Ann. Appl. Probab. 5 875-896. MR1384357
    • (1995) Ann. Appl. Probab , vol.5 , pp. 875-896
    • ASMUSSEN, S.1    GLYNN, P.2    PITMAN, J.3
  • 4
    • 65349179238 scopus 로고    scopus 로고
    • ATTOUCH, H. (1984). Variational Convergence for Functions and Operators. Pitman (Advanced Publishing Program), Boston, MA. MR0773850
    • ATTOUCH, H. (1984). Variational Convergence for Functions and Operators. Pitman (Advanced Publishing Program), Boston, MA. MR0773850
  • 5
    • 65349083367 scopus 로고    scopus 로고
    • BECK, A. (1963). On the strong law of large numbers. In Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961) 21-53. Academic Press, New York. MR0160256
    • BECK, A. (1963). On the strong law of large numbers. In Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961) 21-53. Academic Press, New York. MR0160256
  • 6
    • 40249085367 scopus 로고    scopus 로고
    • A factorisation of diffusion measure and finite sample path constructions
    • MR2394037
    • BESKOS, A., PAPASPILIOPOULOS, O. and ROBERTS, G. O. (2008). A factorisation of diffusion measure and finite sample path constructions. Methodol. Comput. Appl. Probab. 10 85-104. MR2394037
    • (2008) Methodol. Comput. Appl. Probab , vol.10 , pp. 85-104
    • BESKOS, A.1    PAPASPILIOPOULOS, O.2    ROBERTS, G.O.3
  • 7
    • 35349014465 scopus 로고    scopus 로고
    • Retrospective exact simulation of diffusion sample paths with applications
    • MR2274855
    • BESKOS, A., PAPASPILIOPOULOS, O. andROBERTS, G. O. (2006). Retrospective exact simulation of diffusion sample paths with applications. Bernoulli 12 1077-1098. MR2274855
    • (2006) Bernoulli , vol.12 , pp. 1077-1098
    • BESKOS, A.1    PAPASPILIOPOULOS, O.2    andROBERTS, G.O.3
  • 8
    • 33646690994 scopus 로고    scopus 로고
    • Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)
    • MR2278331
    • BESKOS, A., PAPASPILIOPOULOS, O., ROBERTS, G. O. and FEARNHEAD, P. (2006). Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 68 1-29. MR2278331
    • (2006) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.68 , pp. 1-29
    • BESKOS, A.1    PAPASPILIOPOULOS, O.2    ROBERTS, G.O.3    FEARNHEAD, P.4
  • 9
    • 30844458345 scopus 로고    scopus 로고
    • Exact simulation of diffusions
    • MR2187299
    • BESKOS, A. and ROBERTS, G. O. (2005). Exact simulation of diffusions. Ann. Appl. Probab. 15 2422-2444. MR2187299
    • (2005) Ann. Appl. Probab , vol.15 , pp. 2422-2444
    • BESKOS, A.1    ROBERTS, G.O.2
  • 10
    • 84972534141 scopus 로고
    • Martingale estimation functions for discretely observed diffusion processes
    • MR1354454
    • BIBBY, B. M. and SØRENSEN, M. (1995). Martingale estimation functions for discretely observed diffusion processes. Bernoulli 1 17-39. MR1354454
    • (1995) Bernoulli , vol.1 , pp. 17-39
    • BIBBY, B.M.1    SØRENSEN, M.2
  • 11
    • 65349148703 scopus 로고    scopus 로고
    • BURKE, G. (1965). A uniform ergodic theorem. Ann. Math. Statist. 36 1853-1858. MR0183001
    • BURKE, G. (1965). A uniform ergodic theorem. Ann. Math. Statist. 36 1853-1858. MR0183001
  • 12
    • 0036900791 scopus 로고    scopus 로고
    • On the convergence of the Monte Carlo maximum likelihood method for latent variable models
    • MR1988415
    • CAPPÉ, O., DOUC, R., MOULINES, E. and ROBERT, C. (2002). On the convergence of the Monte Carlo maximum likelihood method for latent variable models. Scand. J. Statist. 29 615-635. MR1988415
    • (2002) Scand. J. Statist , vol.29 , pp. 615-635
    • CAPPÉ, O.1    DOUC, R.2    MOULINES, E.3    ROBERT, C.4
  • 13
    • 0037251443 scopus 로고    scopus 로고
    • A functional version of the Birkhoff ergodic theorem for a normal integrand: A variational approach
    • MR1959786
    • CHOIRAT, C.,HESS, C. and SERI, R. (2003). A functional version of the Birkhoff ergodic theorem for a normal integrand: A variational approach. Ann. Probab. 31 63-92. MR1959786
    • (2003) Ann. Probab , vol.31 , pp. 63-92
    • CHOIRAT, C.1    HESS, C.2    SERI, R.3
  • 14
    • 65349146685 scopus 로고    scopus 로고
    • DEVROYE, L. (1986). Nonuniform Random Variate Generation. Springer, New York. MR0836973
    • DEVROYE, L. (1986). Nonuniform Random Variate Generation. Springer, New York. MR0836973
  • 15
    • 65349147292 scopus 로고    scopus 로고
    • DUDLEY, R. M. (1999). Uniform Central Limit Theorems. Cambridge Univ. Press. MR1720712
    • DUDLEY, R. M. (1999). Uniform Central Limit Theorems. Cambridge Univ. Press. MR1720712
  • 16
    • 0036339461 scopus 로고    scopus 로고
    • Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes (with discussion)
    • MR1939904
    • DURHAM, G. B. andGALLANT, A. R. (2002). Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes (with discussion). J. Bus. Econom. Statist. 20 297-338. MR1939904
    • (2002) J. Bus. Econom. Statist , vol.20 , pp. 297-338
    • DURHAM, G.B.1    andGALLANT, A.R.2
  • 17
    • 0000440935 scopus 로고    scopus 로고
    • Likelihood inference for discretely observed nonlinear diffusions
    • MR1839375
    • ELERIAN, O., CHIB, S. and SHEPHARD, N. (2001). Likelihood inference for discretely observed nonlinear diffusions. Econometrica 69 959-993. MR1839375
    • (2001) Econometrica , vol.69 , pp. 959-993
    • ELERIAN, O.1    CHIB, S.2    SHEPHARD, N.3
  • 18
    • 0035586814 scopus 로고    scopus 로고
    • MCMC analysis of diffusion models with application to finance
    • MR1939708
    • ERAKER, B. (2001). MCMC analysis of diffusion models with application to finance. J. Bus. Econom. Statist. 19 177-191. MR1939708
    • (2001) J. Bus. Econom. Statist , vol.19 , pp. 177-191
    • ERAKER, B.1
  • 19
    • 65349162994 scopus 로고    scopus 로고
    • FERGUSON, T. S. (1996). A Course in Large Sample Theory. Chapman and Hall, London. MR1699953
    • FERGUSON, T. S. (1996). A Course in Large Sample Theory. Chapman and Hall, London. MR1699953
  • 20
    • 18544376108 scopus 로고    scopus 로고
    • Which moments to match?
    • MR1422547
    • GALLANT, A. R. and TAUCHEN, G. (1996). Which moments to match? Econometric Theory 12 657-681. MR1422547
    • (1996) Econometric Theory , vol.12 , pp. 657-681
    • GALLANT, A.R.1    TAUCHEN, G.2
  • 21
    • 0000529797 scopus 로고
    • On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
    • MR1204521
    • GENON-CATALOT, V. and JACOD, J. (1993). On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. Ann. Inst. H. Poincaré Probab. Statist. 29 119-151. MR1204521
    • (1993) Ann. Inst. H. Poincaré Probab. Statist , vol.29 , pp. 119-151
    • GENON-CATALOT, V.1    JACOD, J.2
  • 22
    • 0000106855 scopus 로고
    • On the convergence of Monte Carlo maximum likelihood calculations
    • MR1257812
    • GEYER, C. J. (1994). On the convergence of Monte Carlo maximum likelihood calculations. J. Roy. Statist. Soc. Ser. B 56 261-274. MR1257812
    • (1994) J. Roy. Statist. Soc. Ser. B , vol.56 , pp. 261-274
    • GEYER, C.J.1
  • 23
    • 0000051109 scopus 로고
    • Constrained Monte Carlo maximum likelihood for dependent data (with discussion)
    • MR1185217
    • GEYER, C. J. and THOMPSON, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. Roy. Statist. Soc. Ser. B 54 657-699. MR1185217
    • (1992) J. Roy. Statist. Soc. Ser. B , vol.54 , pp. 657-699
    • GEYER, C.J.1    THOMPSON, E.A.2
  • 24
    • 65349092166 scopus 로고    scopus 로고
    • GIESY, D. P. (1976). Strong laws of large numbers for independent sequences of Banach spacevalued random variables. In Probability in Banach Spaces (Proc. First Internat. Conf., Oberwolfach, 1975) 89-99. Lecture Notes in Math. 526. Springer, Berlin. MR0440673
    • GIESY, D. P. (1976). Strong laws of large numbers for independent sequences of Banach spacevalued random variables. In Probability in Banach Spaces (Proc. First Internat. Conf., Oberwolfach, 1975) 89-99. Lecture Notes in Math. 526. Springer, Berlin. MR0440673
  • 26
    • 65349089683 scopus 로고    scopus 로고
    • HALL, P. and HEYDE, C. C. (1980). Martingale Limit Theory and Its Application. Academic Press, New York. MR0624435
    • HALL, P. and HEYDE, C. C. (1980). Martingale Limit Theory and Its Application. Academic Press, New York. MR0624435
  • 27
    • 0035995078 scopus 로고    scopus 로고
    • Computational aspects related to martingale estimating functions for a discretely observed diffusion
    • MR1925568
    • KESSLER, M. and PAREDES, S. (2002). Computational aspects related to martingale estimating functions for a discretely observed diffusion. Scand. J. Statist. 29 425-440. MR1925568
    • (2002) Scand. J. Statist , vol.29 , pp. 425-440
    • KESSLER, M.1    PAREDES, S.2
  • 28
    • 65349169122 scopus 로고    scopus 로고
    • KINGMAN, J. F. C. (1993). Poisson Processes. Oxford Univ. Press, New York. MR1207584
    • KINGMAN, J. F. C. (1993). Poisson Processes. Oxford Univ. Press, New York. MR1207584
  • 29
    • 65349150818 scopus 로고    scopus 로고
    • KLOEDEN, P. E. and PLATEN, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer, Berlin. MR1214374
    • KLOEDEN, P. E. and PLATEN, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer, Berlin. MR1214374
  • 30
    • 0005079237 scopus 로고
    • Eléments aléatoires dans un espace de Banach.
    • MR0064339
    • MOURIER, E. (1953). Eléments aléatoires dans un espace de Banach. Ann. Inst. H. Poincaré 13 161-244. MR0064339
    • (1953) Ann. Inst. H. Poincaré , vol.13 , pp. 161-244
    • MOURIER, E.1
  • 31
    • 65349190190 scopus 로고    scopus 로고
    • ∅KSENDAL, B. (2003). Stochastic Differential Equations, 6th ed. Springer, Berlin. MR2001996
    • ∅KSENDAL, B. (2003). Stochastic Differential Equations, 6th ed. Springer, Berlin. MR2001996
  • 32
    • 84972530323 scopus 로고
    • Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes
    • MR1363541
    • PEDERSEN, A. R. (1995). Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes. Bernoulli 1 257-279. MR1363541
    • (1995) Bernoulli , vol.1 , pp. 257-279
    • PEDERSEN, A.R.1
  • 33
    • 65349098170 scopus 로고    scopus 로고
    • PESKIR, G. (2000). From Uniform Laws of Large Numbers to Uniform Ergodic Theorems. Univ. Aarhus, Dept. Mathematics. MR1805157
    • PESKIR, G. (2000). From Uniform Laws of Large Numbers to Uniform Ergodic Theorems. Univ. Aarhus, Dept. Mathematics. MR1805157
  • 35
    • 10244252366 scopus 로고    scopus 로고
    • On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm
    • MR1859397
    • ROBERTS, G. O. and STRAMER, O. (2001). On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm. Biometrika 88 603-621. MR1859397
    • (2001) Biometrika , vol.88 , pp. 603-621
    • ROBERTS, G.O.1    STRAMER, O.2
  • 36
    • 0000094976 scopus 로고
    • The joint density of the maximum and its location for a Wiener process with drift
    • MR0531776
    • SHEPP, L. A. (1979). The joint density of the maximum and its location for a Wiener process with drift. J. Appl. Probab. 16 423-427. MR0531776
    • (1979) J. Appl. Probab , vol.16 , pp. 423-427
    • SHEPP, L.A.1
  • 37
    • 10244220000 scopus 로고    scopus 로고
    • Parametric inference for diffusion processes observed at discrete points in time: A survey
    • SØRENSEN, H. (2004). Parametric inference for diffusion processes observed at discrete points in time: A survey. Internat. Statist. Rev. 72 337-354.
    • (2004) Internat. Statist. Rev , vol.72 , pp. 337-354
    • SØRENSEN, H.1
  • 38
    • 0000080373 scopus 로고
    • The Glivenko-Cantelli problem
    • MR0893902
    • TALAGRAND, M. (1987). The Glivenko-Cantelli problem. Ann. Probab. 15 837-870. MR0893902
    • (1987) Ann. Probab , vol.15 , pp. 837-870
    • TALAGRAND, M.1
  • 39
    • 0009452588 scopus 로고
    • A generalization of the Glivenko-Cantelli theorem
    • MR0107891
    • TUCKER, H. G. (1959). A generalization of the Glivenko-Cantelli theorem. Ann. Math. Statist. 30 828-830. MR0107891
    • (1959) Ann. Math. Statist , vol.30 , pp. 828-830
    • TUCKER, H.G.1
  • 40
    • 0000167944 scopus 로고
    • Note on the consistency of the maximum likelihood estimate
    • MR0032169
    • WALD, A. (1949). Note on the consistency of the maximum likelihood estimate. Ann. Math. Statistics 20 595-601. MR0032169
    • (1949) Ann. Math. Statistics , vol.20 , pp. 595-601
    • WALD, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.