Parametric estimation for a parabolic linear SPDE model based on discrete observations

Kaino, Yusuke; Uchida, Masayuki

doi:10.1016/j.jspi.2020.05.004

Cited by 23 publications

(23 citation statements)

References 24 publications

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“…Statistical inference for SPDE models based on discrete observations has been studied by many researchers, see, for example, Markussen [19], Bibinger and Trabs [1], Chong [3], [2], Cialenco et al [5], Cialenco and Huang [7], Hildebrandt [9], Kaino and Uchida [13] and references therein. Recently, Kaino and Uchida [14] proposed the adaptive maximum likelihood type estimation for the coefficient parameters of linear parabolic second-order SPDEs in one space dimension with a small noise.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data

Tonaki¹,

Kaino²,

Uchida³

2022

Preprint

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We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by two types Q-Wiener processes based on high frequency data in time and space. We first estimate the parameters which appear in the coordinate process of the SPDE using the minimum contrast estimator based on the thinned data with respect to space, and then construct an approximate coordinate process of the SPDE. Furthermore, we propose estimators of the coefficient parameters of the SPDE utilizing the approximate coordinate process based on the thinned data with respect to time. We also give some simulation results.

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Section: Introductionmentioning

confidence: 99%

Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data

Tonaki¹,

Kaino²,

Uchida³

2022

Preprint

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“…Compared to the thinning method of [22], this rate is a considerable improvement. Indeed, it is (almost) optimal in the minimax sense, as shown in Section 5.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…We conclude this section by remarking that estimation of all four parameters (σ 2 , ϑ 2 , ϑ 1 , ϑ 0 ), which requires T → ∞, is treated in Markussen [28] from a time series perspective and in Kaino and Uchida [22] as well as Hildebrandt [15], assuming high frequency observations in time and space.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…Assuming X is observed on a discrete grid {(t i , y k )} i=0,...,N,k=0,...,M ⊂ [0, T ] × [0, 1], approximate maximum likelihood estimators have been first investigated by Markussen [28] for T → ∞. For various linear SPDEs central limit theorems for method of moment type estimators based on realized quadratic variations have been studied by Torres et al [36], Cialenco and Huang [7], Cialenco and Kim [8], Bibinger and Trabs [2,3], Chong [4,5], Shevchenko et al [35], Liu and Tudor [25], as well as Kaino and Uchida [22]. However, all these works only give partial answers to the estimation problem.…”

Section: Introductionmentioning

confidence: 99%

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Parameter estimation for SPDEs based on discrete observations in time and space

Hildebrandt

Trabs

2021

Electron. J. Statist.

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Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in both coordinates, we prove central limit theorems for realized quadratic variations based on temporal and spatial increments as well as on double increments in time and space. Resulting method of moments estimators for the diffusivity and the volatility parameter inherit the asymptotic normality and can be constructed robustly with respect to the sampling frequencies in time and space. Upper and lower bounds reveal that in general the optimal convergence rate for joint estimation of the parameters is slower than the usual parametric rate. The theoretical results are illustrated in a numerical example.

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“…In these articles estimators based on power variations of time-increments of the solution were constructed and central limit theorems were proved. In [24] an adaptive maximum likelihood type estimator of the coefficient parameter was proposed for a parabolic linear second order SPDE. However, there are still basic questions which are not settled in the statistical literature on SPDEs, see the recent review [13] for details.…”

Section: Introductionmentioning

confidence: 99%

Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation

Avetisian¹,

Ralchenko²

2020

Modern Stochastics: Theory and Applications

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Parametric estimation for a parabolic linear SPDE model based on discrete observations

Cited by 23 publications

References 24 publications

Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data

Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data

Parameter estimation for SPDEs based on discrete observations in time and space

Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation

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