Parameter estimation in linear filtering

Kallianpur, G.; Selukar, Rajesh

doi:10.1016/0047-259x(91)90102-8

Cited by 17 publications

(9 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For continuous time linear systems such as (1)- (2) with constant functions f (ϑ, t) = f (ϑ) , a (ϑ, t) = a (ϑ) , b (ϑ, t) = b (ϑ) , σ (t) = σ, (ε = 1, ψ ε = 1), asymptotic analysis with respect to T → ∞ appeared in [18], [13], [24]. The survey [25] reviews some results on parameter estimation in the model ( 1)- (2) in both large time and small noise asymptotics.…”

Section: Introductionmentioning

confidence: 99%

Hidden Markov Model Where Higher Noise Makes Smaller Errors

Kutoyants

2020

Preprint

View full text Add to dashboard Cite

We consider the problem of parameter estimation in a partially observed linear Gaussian system with small noises in the state and observation equations. We describe asymptotic properties of the MLE and Bayes estimators in the setting with state and observation noises of possibly unequal intensities. It is shown that both estimators are consistent, asymptotically normal with convergent moments and asymptotically efficient. This model has an unusual feature: larger noise in the state equation yields smaller estimation error. The proofs are based on asymptotic analysis of the Kalman-Bucy filter and the associated Riccati equation in particular.

show abstract

Section: Introductionmentioning

confidence: 99%

Hidden Markov Model Where Higher Noise Makes Smaller Errors

Kutoyants

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…(1) For general linear SDEs two kinds of drift estimators are intensively studied in the literature [1,2,9,10,13]: The Maximum Likelihood (cf. [6] for noisy observations) and Bayes estimators. But the latter differ from those considered here: Instead of (1.3) it is usually assumed that X t is observed without measurement error, cf.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of Bayes estimators for Gaussian Itô-processes with noisy observations

Deck

2006

Journal of Multivariate Analysis

View full text Add to dashboard Cite

show abstract

“…The filtering approach to parameter estimation is a known concept: For linear filtering see [22,36]. Nonlinear filtering in discrete time based on a stochastic representation formula is discussed in [15] (with regular diffusion matrix).…”

Section: Introductionmentioning

confidence: 99%

Robust Parameter Estimation for Stochastic Differential Equations

Deck

Theting

2004

Acta Appl Math

View full text Add to dashboard Cite

We consider the estimation of parameters in stochastic differential equations (SDEs). The problem is treated in the setting of nonlinear filtering theory with a degenerate diffusion matrix. A robust stochastic Feynman-Kac representation for solutions of SDEs of Zakai-type is derived. It is verified that these solutions are conditional densities for the conditional measures defined by degenerate filtering problems. We show that the corresponding estimator for the parameters is robust in the following sense: It depends continuously on both the measurement path and on the intensity of the measurement noise. An algorithm based on a Monte-Carlo approach is given for the practical application of the estimator, and numerical results are reported. Mathematics Subject Classifications (2000): Primary: 62M05, 62M20; secondary: 62F15.

show abstract

Parameter estimation in linear filtering

Cited by 17 publications

References 1 publication

Hidden Markov Model Where Higher Noise Makes Smaller Errors

Hidden Markov Model Where Higher Noise Makes Smaller Errors

Asymptotic properties of Bayes estimators for Gaussian Itô-processes with noisy observations

Robust Parameter Estimation for Stochastic Differential Equations

Contact Info

Product

Resources

About