Displaying similar documents to “Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process”

Hurwicz's estimator of the autoregressive model with non-normal innovations

Youcef Berkoun, Hocine Fellag (2011)

Applicationes Mathematicae

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Using the Bahadur representation of a sample quantile for m-dependent and strong mixing random variables, we establish the asymptotic distribution of the Hurwicz estimator for the coefficient of autoregression in a linear process with innovations belonging to the domain of attraction of an α-stable law (1 < α < 2). The present paper extends Hurwicz's result to the autoregressive model.

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

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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...

On cumulative process model and its statistical analysis

Petr Volf (2000)

Kybernetika

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The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator...

Development of the kriging method with application

Pavel Krejčíř (2002)

Applications of Mathematics

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This paper describes a modification of the kriging method for working with the square root transformation of a spatial random process. We have developed this method for the situation where the spatial process observed is not supposed to be stationary but the assumption is that its square root is a second order stationary spatial random process. Consequently this method is developed for estimating the integral of the process observed and finally some application of the method is given...

Estimation of summary characteristics from replicated spatial point processes

Zbyněk Pawlas (2011)

Kybernetika

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Summary characteristics play an important role in the analysis of spatial point processes. We discuss various approaches to estimating summary characteristics from replicated observations of a stationary point process. The estimators are compared with respect to their integrated squared error. Simulations for three basic types of point processes help to indicate the best way of pooling the subwindow estimators. The most appropriate way depends on the particular summary characteristic,...