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.
@article{1013203463,
author = {Galtchouk, L. and Konev, V.},
title = {On sequential estimation of parameters in semimartingale
regression models with continuous time parameter},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1508-1536},
language = {en},
url = {http://dml.mathdoc.fr/item/1013203463}
}
Galtchouk, L.; Konev, V. On sequential estimation of parameters in semimartingale
regression models with continuous time parameter. Ann. Statist., Tome 29 (2001) no. 2, pp. 1508-1536. http://gdmltest.u-ga.fr/item/1013203463/