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Parameter estimation in linear filtering

Author

Listed:
  • Kallianpur, G.
  • Selukar, R. S.

Abstract

Suppose on a probability space ([Omega], F, P), a partially observable random process (xt, yt), t >= 0; is given where only the second component (yt) is observed. Furthermore assume that (xt, yt) satisfy the following system of stochastic differential equations driven by independent Wiener processes (W1(t)) and (W2(t)): dxt=-[beta]xtdt+dW1(t), x0=0, dyt=[alpha]xtdt+dW2(t), y0=0; [alpha], [beta][infinity](a,b), a>0. We prove the local asymptotic normality of the model and obtain a large deviation inequality for the maximum likelihood estimator (m.l.e.) of the parameter [theta] = ([alpha], [beta]). This also implies the strong consistency, efficiency, asymptotic normality and the convergence of moments for the m.l.e. The method of proof can be easily extended to obtain similar results when vector valued instead of one-dimensional processes are considered and [theta] is a k-dimensional vector.

Suggested Citation

  • Kallianpur, G. & Selukar, R. S., 1991. "Parameter estimation in linear filtering," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 284-304, November.
    • Handle: RePEc:eee:jmvana:v:39:y:1991:i:2:p:284-304
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    Cited by:

    1. Küchler, Uwe & Kutoyants, Yuri A., 1998. "Delay estimation for some stationary diffusion-type processes," SFB 373 Discussion Papers 1998,47, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Mandrekar, V. & Naik-Nimbalkar, U.V., 2009. "Identification of a Markovian system with observations corrupted by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 965-968, April.
    3. Deck, T., 2006. "Asymptotic properties of Bayes estimators for Gaussian Itô-processes with noisy observations," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 563-573, February.
    4. Yury A. Kutoyants, 2021. "On localization of source by hidden Gaussian processes with small noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 671-702, August.

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