Currently displaying 1 – 6 of 6

Showing per page

Order by Relevance | Title | Year of publication

A sharp analysis on the asymptotic behavior of the Durbin–Watson statistic for the first-order autoregressive process

Bernard Bercu;  Frédéric Proïa — 2013

ESAIM: Probability and Statistics

The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin–Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise....

Sharp large deviations for Gaussian quadratic forms with applications

Bernard Bercu;  Fabrice Gamboa;  Marc Lavielle — 2010

ESAIM: Probability and Statistics

Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process, and finally of the empirical...

Page 1

Download Results (CSV)