About the asymptotic behaviour of multidimensional Gaussian martingales and estimates in normal linear regression

Darwich, A. R.; Breton, Alain

doi:10.1016/0167-7152(91)90099-d

Cited by 5 publications

(2 citation statements)

References 5 publications

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“…This model was studied for example in Darwich (1989Darwich ( , 2002; Le Breton and Musiela (1986); Darwich and Le Breton (1991). Kutoyants (2004) studied the problem of parameter estimation in a more general frame using different techniques like likelihood estimation and minimum distance estimation.…”

Section: Introductionmentioning

confidence: 98%

Asymptotic Properties of the LS-estimator of a Gaussian Autoregressive Process by an Averaging Method

Fathallah

2013

Communications in Statistics - Theory and Methods

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This article deals with the problem of parameter estimation of a continuous-time p-dimensional Gaussian autoregressive process. In the stable case, we combine averaging and weighting methods to establish, for the weighted LS-estimator (least-squares estimator)˜ of , an almost-sure central limit theorem (ASCLT), a quadratic strong law (QSL) and a central limit theorem (CLT) associated to the QSL with arithmetic convergence rates. In the unstable case, we establish for the LS-estimatorˆ of , the same optimal asymptotic properties with arithmetic convergence rates. In both cases, using the QSL property, we construct a new estimator of the noise covariance 2 and we specify its weak convergence rates.

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Section: Introductionmentioning

confidence: 98%

Asymptotic Properties of the LS-estimator of a Gaussian Autoregressive Process by an Averaging Method

Fathallah

2013

Communications in Statistics - Theory and Methods

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“…The results on asymptotic theory of estimates of parameters in linear stochastic differential equations driven by the Wiener processes are given in Arato, Kolmogorov and Sinai (1962), Le Breton (1977), Liptser and Shiryaev (1977) and Jankunas and Khasminskii (1997), among others. Estimation problems for stochastic differential equations driven by martingale noise are considered in Novikov (1984), Christopeit (1986) and Darwich and Le Breton (1991).…”

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confidence: 99%

On sequential estimation of parameters in semimartingale regression models with continuous time parameter

Galtchouk¹,

Konev²

2001

Ann. Statist.

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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.

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On Sequential Estimation of Parameters for Linear Regression with Martingale Noise

Galtchouk¹

1998

Contributions to Statistics

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About the asymptotic behaviour of multidimensional Gaussian martingales and estimates in normal linear regression

Cited by 5 publications

References 5 publications

Asymptotic Properties of the LS-estimator of a Gaussian Autoregressive Process by an Averaging Method

Asymptotic Properties of the LS-estimator of a Gaussian Autoregressive Process by an Averaging Method

On sequential estimation of parameters in semimartingale regression models with continuous time parameter

On Sequential Estimation of Parameters for Linear Regression with Martingale Noise

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