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Volumn 11, Issue 3, 2005, Pages 411-444

Exact asymptotics for estimating the marginal density of discretely observed diffusion processes

Author keywords

Density estimation; Dependent data; Diffusion processes; Discrete sampling; Exact asymptotics; Minimax risk; Nonparametric estimation

Indexed keywords


EID: 33845771345     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1120591183     Document Type: Article
Times cited : (5)

References (55)
  • 1
    • 0030369366 scopus 로고    scopus 로고
    • Nonparametric pricing of interest rate derivative securities
    • Aït-Sahalia, Y. (1996a) Nonparametric pricing of interest rate derivative securities. Econometrica, 64, 527-560.
    • (1996) Econometrica , vol.64 , pp. 527-560
    • Aït-Sahalia, Y.1
  • 2
    • 0242670422 scopus 로고    scopus 로고
    • Testing continuous-time models of the spot interest rate
    • Aït-Sahalia, Y. (1996b) Testing continuous-time models of the spot interest rate. Rev. Financial Stud., 9, 385-426.
    • (1996) Rev. Financial Stud. , vol.9 , pp. 385-426
    • Aït-Sahalia, Y.1
  • 4
    • 0242473322 scopus 로고
    • Densité des diffusions en temps petit: Développements asymptotiques. I
    • J. Azéma and M. Yor (eds), Lecture Notes in Math. 1059. Berlin: Springer-Verlag
    • Azencott, R. (1984) Densité des diffusions en temps petit: développements asymptotiques. I. In J. Azéma and M. Yor (eds), Séminaire de Probabilités XVIII, Lecture Notes in Math. 1059, pp. 402-498. Berlin: Springer-Verlag.
    • (1984) Séminaire de Probabilités XVIII , pp. 402-498
    • Azencott, R.1
  • 5
    • 0000741389 scopus 로고
    • Nonparametric identification for diffusion processes
    • Banon, G. (1978) Nonparametric identification for diffusion processes. SIAM J. Control Optim., 16, 380-395.
    • (1978) SIAM J. Control Optim. , vol.16 , pp. 380-395
    • Banon, G.1
  • 6
    • 0019610554 scopus 로고
    • Recursive estimation in diffusion model
    • Banon, G. and Nguyen, H.T. (1981) Recursive estimation in diffusion model. SIAM J. Control Optim., 19, 676-685.
    • (1981) SIAM J. Control Optim. , vol.19 , pp. 676-685
    • Banon, G.1    Nguyen, H.T.2
  • 7
    • 0042227270 scopus 로고    scopus 로고
    • Efficient estimation of analytic density under random censorship
    • Belitser, E. (1998) Efficient estimation of analytic density under random censorship. Bernoulli, 4, 519-543.
    • (1998) Bernoulli , vol.4 , pp. 519-543
    • Belitser, E.1
  • 10
    • 38249043318 scopus 로고
    • On smoothed probability density estimation for stationary processes
    • Castellana, J.V. and Leadbetter, M.R. (1986) On smoothed probability density estimation for stationary processes. Stochastic Process. Appl., 21, 179-193.
    • (1986) Stochastic Process. Appl. , vol.21 , pp. 179-193
    • Castellana, J.V.1    Leadbetter, M.R.2
  • 11
    • 28644449009 scopus 로고    scopus 로고
    • Asymptotically efficient trend coefficient estimation for ergodic diffusion
    • Dalalyan, A.S. and Kutoyants, Yu.A. (2002) Asymptotically efficient trend coefficient estimation for ergodic diffusion. Math. Methods Statist., 11, 402-427.
    • (2002) Math. Methods Statist. , vol.11 , pp. 402-427
    • Dalalyan, A.S.1    Kutoyants, Yu.A.2
  • 12
    • 21344480943 scopus 로고
    • Asymptotic minimax risk for sup-norm loss: Solution via optimal recovery
    • Donoho, D.L. (1994) Asymptotic minimax risk for sup-norm loss: Solution via optimal recovery. Probab. Theory Related Fields, 99, 145-170.
    • (1994) Probab. Theory Related Fields , vol.99 , pp. 145-170
    • Donoho, D.L.1
  • 13
    • 0003614268 scopus 로고
    • Lecture Notes in Statist. 85. New York: Springer-Verlag
    • Doukhan, R (1994) Mixing: Properties and Examples, Lecture Notes in Statist. 85. New York: Springer-Verlag.
    • (1994) Mixing: Properties and Examples
    • Doukhan, R.1
  • 15
    • 0010052178 scopus 로고
    • Estimating a square integrable spectral density from a sequence of observations
    • Efromovich, S.Yu. and Pinsker, M.S. (1982) Estimating a square integrable spectral density from a sequence of observations. Problems Inform. Transmission, 17, 182-196.
    • (1982) Problems Inform. Transmission , vol.17 , pp. 182-196
    • Efromovich, S.Yu.1    Pinsker, M.S.2
  • 16
    • 0020152606 scopus 로고
    • Estimation of square-integrable probability density of a random variable
    • Efromovich, S.Yu. and Pinsker, M.S. (1983) Estimation of square-integrable probability density of a random variable. Problems Inform. Transmission, 18, 175-189.
    • (1983) Problems Inform. Transmission , vol.18 , pp. 175-189
    • Efromovich, S.Yu.1    Pinsker, M.S.2
  • 18
    • 0036334160 scopus 로고    scopus 로고
    • LAN property for ergodic diffusions with discrete observations
    • Gobet, E. (2002) LAN property for ergodic diffusions with discrete observations. Ann. Inst. H. Poincaré Probab. Statist., 38, 711-737.
    • (2002) Ann. Inst. H. Poincaré Probab. Statist. , vol.38 , pp. 711-737
    • Gobet, E.1
  • 20
    • 0023207865 scopus 로고
    • Adaptive asymptotically minimax estimators of smooth signals
    • Golubev, G.K. (1987) Adaptive asymptotically minimax estimators of smooth signals. Problems Inform. Transmission, 23, 47-55.
    • (1987) Problems Inform. Transmission , vol.23 , pp. 47-55
    • Golubev, G.K.1
  • 21
    • 0000893122 scopus 로고    scopus 로고
    • Asymptotically efficient estimation for analytic distributions
    • Golubev, G.K. and Levit, B.Y. (1996) Asymptotically efficient estimation for analytic distributions. Math. Methods Statist., 5, 357-368.
    • (1996) Math. Methods Statist. , vol.5 , pp. 357-368
    • Golubev, G.K.1    Levit, B.Y.2
  • 22
    • 0000029133 scopus 로고
    • A risk bound in Sobolev class regression
    • Golubev, G.K. and Nussbaum, M. (1990) A risk bound in Sobolev class regression. Ann. Statist., 18, 758-778.
    • (1990) Ann. Statist. , vol.18 , pp. 758-778
    • Golubev, G.K.1    Nussbaum, M.2
  • 23
    • 0001552467 scopus 로고    scopus 로고
    • Asymptotically efficient estimation of analytic functions in Gaussian noise
    • Golubev, Y.K., Levit, B.Y. and Tsybakov, A.B. (1996) Asymptotically efficient estimation of analytic functions in Gaussian noise. Bernoulli, 2, 167-181.
    • (1996) Bernoulli , vol.2 , pp. 167-181
    • Golubev, Y.K.1    Levit, B.Y.2    Tsybakov, A.B.3
  • 25
    • 0010661898 scopus 로고    scopus 로고
    • Spectral methods for identifying scalar diffusions
    • Hansen, L.P., Scheinkman, J.A. and Touzi, N. (1998) Spectral methods for identifying scalar diffusions. J. Econometrics, 86, 1-32.
    • (1998) J. Econometrics , vol.86 , pp. 1-32
    • Hansen, L.P.1    Scheinkman, J.A.2    Touzi, N.3
  • 26
    • 0000806381 scopus 로고    scopus 로고
    • p estimation of the diffusion coefficient
    • p estimation of the diffusion coefficient. Bernoulli, 5, 447-481.
    • (1999) Bernoulli , vol.5 , pp. 447-481
    • Hoffmann, M.1
  • 27
    • 3142779593 scopus 로고    scopus 로고
    • Estimation of analytic functions
    • M. de Gunst, C. Klaassen and A. van der Vaart (eds), IMS Lecture Notes Monogr. Ser. Beachwoord, OH: Institute of Mathematical Statistics
    • Ibragimov, I. (2001) Estimation of analytic functions. In M. de Gunst, C. Klaassen and A. van der Vaart (eds), State of the Art in Probability and Statistics: Festschrift for Willem R. van Zwet, IMS Lecture Notes Monogr. Ser, 36, pp. 359-383. Beachwoord, OH: Institute of Mathematical Statistics.
    • (2001) State of the Art in Probability and Statistics: Festschrift for Willem R. Van Zwet , vol.36 , pp. 359-383
    • Ibragimov, I.1
  • 30
    • 0040360923 scopus 로고    scopus 로고
    • Estimation of an ergodic diffusion from discrete observations
    • Kessler, M. (1997) Estimation of an ergodic diffusion from discrete observations. Scand. J. Statist., 24, 211-229.
    • (1997) Scand. J. Statist. , vol.24 , pp. 211-229
    • Kessler, M.1
  • 31
    • 0000647626 scopus 로고    scopus 로고
    • Estimating equations based on eigenfunctions for a discretely observed diffusion process
    • Kessler, M. and Sorensen, M. (1999) Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli, 5, 299-314.
    • (1999) Bernoulli , vol.5 , pp. 299-314
    • Kessler, M.1    Sorensen, M.2
  • 32
    • 0000348715 scopus 로고
    • An asymptotically minimax regression estimator in the uniform norm up to exact constant
    • Korostelev, A.P. (1993) An asymptotically minimax regression estimator in the uniform norm up to exact constant. Theory Probab. Appl., 38, 737-743.
    • (1993) Theory Probab. Appl. , vol.38 , pp. 737-743
    • Korostelev, A.P.1
  • 33
    • 0030514782 scopus 로고    scopus 로고
    • A minimaxity criterion in nonparametric regression based on large-deviations probabilities
    • Korostelev, A.P. (1996) A minimaxity criterion in nonparametric regression based on large-deviations probabilities. Ann. Statist., 24, 1075-1083.
    • (1996) Ann. Statist. , vol.24 , pp. 1075-1083
    • Korostelev, A.P.1
  • 34
    • 0010556576 scopus 로고    scopus 로고
    • Minimax Bahadur efficiency for small confidence levels
    • in Russian
    • Korostelev, A.P. and Leonov, S.L. (1996) Minimax Bahadur efficiency for small confidence levels. Problemy Peredachi Informatsii, 32, 3-15 (in Russian)
    • (1996) Problemy Peredachi Informatsii , vol.32 , pp. 3-15
    • Korostelev, A.P.1    Leonov, S.L.2
  • 35
    • 33845746305 scopus 로고    scopus 로고
    • English translation
    • [English translation: Problems Inform. Transmission, 32, 303-313.]
    • Problems Inform. Transmission , vol.32 , pp. 303-313
  • 36
    • 0042112381 scopus 로고    scopus 로고
    • The asymptotic minimax constant for sup-norm loss in nonparametric density estimation
    • Korostelev, A.P. and Nussbaum, M. (1999) The asymptotic minimax constant for sup-norm loss in nonparametric density estimation. Bernoulli, 5, 1099-1118.
    • (1999) Bernoulli , vol.5 , pp. 1099-1118
    • Korostelev, A.P.1    Nussbaum, M.2
  • 37
    • 0031569253 scopus 로고    scopus 로고
    • Some problems of nonparametric estimation by observations of ergodic diffusion process
    • Kutoyants, Yu.A. (1997) Some problems of nonparametric estimation by observations of ergodic diffusion process. Statist. Probab. Lett., 32, 311-320.
    • (1997) Statist. Probab. Lett. , vol.32 , pp. 311-320
    • Kutoyants, Yu.A.1
  • 38
    • 0141967982 scopus 로고    scopus 로고
    • Density estimation for a class of continuous time processes
    • Leblanc, F. (1997) Density estimation for a class of continuous time processes. Math. Methods Statist., 6, 171-199.
    • (1997) Math. Methods Statist. , vol.6 , pp. 171-199
    • Leblanc, F.1
  • 39
    • 0001633551 scopus 로고    scopus 로고
    • On the solution of an optimal recovery problem and its applications in nonparametric regression
    • Leonov, S.L. (1997) On the solution of an optimal recovery problem and its applications in nonparametric regression. Math. Methods Statist., 6, 476-490.
    • (1997) Math. Methods Statist. , vol.6 , pp. 476-490
    • Leonov, S.L.1
  • 40
    • 0000458553 scopus 로고    scopus 로고
    • Adaptive minimax estimation of infinitely differentiable functions
    • Lepski, O.V and Levit, B.Y. (1998) Adaptive minimax estimation of infinitely differentiable functions. Math. Methods Statist., 7, 123-156.
    • (1998) Math. Methods Statist. , vol.7 , pp. 123-156
    • Lepski, O.V.1    Levit, B.Y.2
  • 41
    • 0043104443 scopus 로고
    • Some limit theorems for large deviations
    • in Russian
    • Nagaev, S.V (1965) Some limit theorems for large deviations. Tear. Veroyatnost i Primenen., 10, 231-254 (in Russian)
    • (1965) Tear. Veroyatnost i Primenen. , vol.10 , pp. 231-254
    • Nagaev, S.V.1
  • 42
    • 33845782457 scopus 로고    scopus 로고
    • English translation
    • [English translation: Theory Probab. Appl., 10, 214-235.]
    • Theory Probab. Appl. , vol.10 , pp. 214-235
  • 43
    • 0032263989 scopus 로고    scopus 로고
    • Strong approximation of density estimators from weakly dependent observations by density estimators from independent observations
    • Neumann, M.H. (1998) Strong approximation of density estimators from weakly dependent observations by density estimators from independent observations. Ann. Statist., 26, 2014-2048.
    • (1998) Ann. Statist. , vol.26 , pp. 2014-2048
    • Neumann, M.H.1
  • 44
    • 0000821694 scopus 로고
    • On the efficiency of wavelet estimators under arbitrary error distributions
    • Neumann, M.H. and Spokoiny, V.G. (1995) On the efficiency of wavelet estimators under arbitrary error distributions. Math. Methods Statist., 4, 137-166.
    • (1995) Math. Methods Statist. , vol.4 , pp. 137-166
    • Neumann, M.H.1    Spokoiny, V.G.2
  • 48
    • 0000056063 scopus 로고
    • Optimal filtration of square-integrable signals in Gaussian noise
    • in Russian
    • Pinsker, M.S. (1980) Optimal filtration of square-integrable signals in Gaussian noise. Problemy Peredachi Informatsii, 16, 52-68 (in Russian)
    • (1980) Problemy Peredachi Informatsii , vol.16 , pp. 52-68
    • Pinsker, M.S.1
  • 49
    • 0000056062 scopus 로고    scopus 로고
    • English translation
    • [English translation: Problems Inform. Transmission, 16, 120-133.]
    • Problems Inform. Transmission , vol.16 , pp. 120-133
  • 50
    • 0001232820 scopus 로고    scopus 로고
    • Subsampling for heteroskedastic time series
    • Politis, D.N., Romano, J.P. and Wolf, M. (1997) Subsampling for heteroskedastic time series. J. Econometrics, 81, 281-317.
    • (1997) J. Econometrics , vol.81 , pp. 281-317
    • Politis, D.N.1    Romano, J.P.2    Wolf, M.3
  • 52
    • 0039731510 scopus 로고    scopus 로고
    • Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process
    • Saavedra, A. and Cao, R. (1999) Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process. Stochastic Process. Appl., 80, 129-155.
    • (1999) Stochastic Process. Appl. , vol.80 , pp. 129-155
    • Saavedra, A.1    Cao, R.2
  • 53
    • 0002603666 scopus 로고    scopus 로고
    • 2-minimax estimation of probability density functions
    • 2-minimax estimation of probability density functions. Math. Methods Statist., 5, 253-274.
    • (1996) Math. Methods Statist. , vol.5 , pp. 253-274
    • Schipper, M.1
  • 55
    • 0000342149 scopus 로고
    • Bounds for the mixing rate in the theory of stochastic equations
    • Veretennikov, A.Yu. (1984) Bounds for the mixing rate in the theory of stochastic equations. Theory Probab. Appl., 32, 273-281.
    • (1984) Theory Probab. Appl. , vol.32 , pp. 273-281
    • Veretennikov, A.Yu.1


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