Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations

Yoshida, Nakahiro

doi:10.1007/s10463-009-0263-z

Cited by 117 publications

(261 citation statements)

References 22 publications

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“…2) see Yoshida [18,19] and Kessler [7]. Here we note that in the correctly specified parametric case,J(θ * ) is the asymptotic Fisher information matrix, see Gobet [4].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The parametric inference for correctly specified ergodic diffusion processes from discrete observations has been studied by many researchers, see Prakasa Rao [14,15], Florens-Zmirou [2], Yoshida [18,19], Bibby and Sørensen [1], Kessler [7] and references therein. Here the correctly specified diffusion model means that there exists a true parameter value θ 0 = (α 0 , β 0 ) ∈ Θ α × Θ β such that b(x, α 0 ) = B(x) and [σσ ](x, β 0 ) = [SS ](x) for all x, where denotes the transpose.…”

Section: Introductionmentioning

confidence: 99%

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Estimation for misspecified ergodic diffusion processes from discrete observations

Uchida

Yoshida

2011

ESAIM: PS

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Abstract. The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the minimum contrast estimator is proved. In particular, the rate of convergence for the minimum contrast estimator of diffusion coefficient parameter in a misspecified model is different from the one in the correctly specified parametric model. Mathematics Subject Classification. 62F12, 62M05, 60J60.

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“…2) see Yoshida [18,19] and Kessler [7]. Here we note that in the correctly specified parametric case,J(θ * ) is the asymptotic Fisher information matrix, see Gobet [4].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation for misspecified ergodic diffusion processes from discrete observations

Uchida

Yoshida

2011

ESAIM: PS

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“…here we used (5.20) [39]. See also Ogihara and Yoshida [21] or Masuda [19] for simplified descriptions for those conditions.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…This means that Z n,ǫ could be Partially Locally Asymptotically Quadratic (PLAQ), which is a starting point of [39]. According to Theorem 3,(c) …”

Section: Proof Of Theoremmentioning

confidence: 99%

Threshold Estimation for Stochastic Processes with Small Noise

Shimizu

2017

Scandinavian J Statistics

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Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data, and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was choosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions.

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“…The above-mentioned theorem ensures the existence of a consistent sequence of M-estimators. On the other hand, it is possible to show the convergence of any sequence of M-estimators with a convergence rate if we apply the polynomial type large deviation inequality (Yoshida 2005).…”

Section: Expansion Formulasmentioning

confidence: 99%

Third-order asymptotic expansion of M-estimators for diffusion processes

Sakamoto

Yoshida

2008

Ann Inst Stat Math

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Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations

Abstract: Large deviation, Quasi-likelihood analysis, Random field, Diffusion process,

Cited by 117 publications

References 22 publications

Estimation for misspecified ergodic diffusion processes from discrete observations

Estimation for misspecified ergodic diffusion processes from discrete observations

Threshold Estimation for Stochastic Processes with Small Noise

Third-order asymptotic expansion of M-estimators for diffusion processes

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