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October 2001 On sequential estimation of parameters in semimartingale regression models with continuous time parameter
L. Galtchouk, V. Konev
Ann. Statist. 29(5): 1508-1536 (October 2001). DOI: 10.1214/aos/1013203463

Abstract

We consider the problem of parameter estimation for multidimensional continuous-time linear stochastic regression models with an arbitrary finite number of unknown parameters and with martingale noise. The main result of the paper claims that the unknown parameters can be estimated with prescribed mean-square precision in this general model providing a unified description of both discrete and continuous time process. Among the conditions on the regressors there is one bounding the growth of the maximal eigenvalue of the design matrix with respect to its minimal eigenvalue. This condition is slightly stronger as compared with the corresponding conditions usually imposed on the regressors in asymptotic investigations but still it enables one to consider models with different behavior of the eigenvalues. The construction makes use of a two-step procedure based on the modified least-squares estimators and special stopping rules.

Citation

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L. Galtchouk. V. Konev. "On sequential estimation of parameters in semimartingale regression models with continuous time parameter." Ann. Statist. 29 (5) 1508 - 1536, October 2001. https://doi.org/10.1214/aos/1013203463

Information

Published: October 2001
First available in Project Euclid: 8 February 2002

zbMATH: 1043.62067
MathSciNet: MR1873340
Digital Object Identifier: 10.1214/aos/1013203463

Subjects:
Primary: 62L12, 62M09

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 5 • October 2001
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