Journal ArticleDOI
About the asymptotic behaviour of multidimensional Gaussian martingales and estimates in normal linear regression
A.R. Darwich,A. Le Breton +1 more
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TLDR
In this paper, a law of iterated logarithm and a large deviation type result for multidimensional Gaussian martingales is established and an application to the asymptotic study of estimates in a normal regression model is discussed.About:
This article is published in Statistics & Probability Letters.The article was published on 1991-10-01. It has received 5 citations till now. The article focuses on the topics: Iterated logarithm & Law of the iterated logarithm.read more
Citations
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Journal ArticleDOI
On sequential estimation of parameters in semimartingale regression models with continuous time parameter
L. Galtchouk,V. Konev +1 more
TL;DR: In this paper, the authors considered 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.
Journal ArticleDOI
About the asymptotic behaviour of continuous vector-valued local martingales and application in multiple linear regression models
TL;DR: In this paper, the authors studied the asymptotic behavior of the process d M ¢ m 1 M, where M is an R n -continuous vector local martingale and m 1 is the inverse of its predictable quadratic variation.
Journal ArticleDOI
Asymptotic Properties of the LS-estimator of a Gaussian Autoregressive Process by an Averaging Method
TL;DR: In this article, the problem of parameter estimation of a continuous-time p-dimensional Gaussian autoregressive process was considered and the convergence rate of the LS-estimator of θ was investigated.
Book ChapterDOI
On Sequential Estimation of Parameters for Linear Regression with Martingale Noise
TL;DR: In this paper, the problem of parameter estimation for continuous-time regression models is considered, and a sequential plan is constructed which enables the estimation of unknown parameters with a given precision.
Journal ArticleDOI
On Stochastic Approximation Procedures with Averaging
A. Le Breton,Alexander Novikov +1 more
TL;DR: In this article, the authors considered linear multidimensional stochastic approximation procedures in continuous time with martingale errors and derived an asymptotic behavior of the estimator obtained by trajectory averaging.
References
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Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.
Book ChapterDOI
Sur le comportement asymptotique des martingales locales
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/legal.php) of the agreement with the séminaire de probabilités (Strasbourg) are discussed.
Journal ArticleDOI
Quasi-least-squares estimation in semimartingale regression models
TL;DR: In this paper, the authors considered a linear regression model with stochastic regressors and local martingale as noise process and showed that under a certain condition limiting the growth of the maximal eigenvalue of the design matrix with respect to the minimal eigen value, this quasi-least-squares estimate converges with probability one to the true parameter values.
Journal ArticleDOI
Laws of large numbers for semimartingales with applications to stochastic regression
A. Le Breton,Marek Musiela +1 more
TL;DR: In this paper, strong laws of large numbers for matrix-normalized vector-valued local martingales are derived from strong laws for positive local submartingales and purely discontinuous local Martingales.