In this article we consider Lévy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample autocorrelations. A comparison with the classical setting of discrete moving average time series shows that in the last case a correction term should be added to the cl...

We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove its consistency and asymptotic normality under mild assumptions. We study the semiparametric likelihood process and prove local asymptotic normality of the ...

The central limit theorem (CLT) for the sample mean of iid rv's is known to be equivalent to the asymptotic normality condition (ANC) of Levy. And Levy's ANC is well known to be equivalent to an alternative ANC of Feller. Both are equivalent to a negligibility requirement, considered by O'Brien. More recently, additional equivalences have been developed in terms of the quantile function, by Cso...

Abstract. In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic statistics (like the number of unrestricted rows, the number of rows, and the number of 1s in the first row) exactly. In all three cases the distribution...

In this paper, we establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the approximate mean squared error of the kernel estimator.

Estimation Gérard BIAU a,∗, Benôıt CADRE b, David M. MASON c and Bruno PELLETIER d a LSTA & LPMA Université Pierre et Marie Curie – Paris VI Bôıte 158, 175 rue du Chevaleret 75013 Paris, France [email protected] b IRMAR, ENS Cachan Bretagne, CNRS, UEB Campus de Ker Lann Avenue Robert Schuman 35170 Bruz, France [email protected] c University of Delaware Food and Resource Econ...

If a random set (binary image) is composed of randomly sized, disjoint translates arising as homothetics of a ®nite number of compact primitives and a granulometry is generated by a convex, compact set, then the granulometric moments of the random set can be expressed in terms of model parameters. This paper shows that, under mild conditions , any ®nite vector of granulometric moments possesses...

To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators /'j and J'2 based on 2N and 4N observations, respec2 2 » tively, of the function. He also considered estimators Dy and D2 of the variances of/j and J'2, respectively. This paper shows that all these estimators are asymptotically normally distributed as N tends to infinity.

This paper proves large-system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the single-user matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both w...

Title of dissertation: ASYMPTOTIC NORMALITY IN GENERALIZED LINEAR MIXED MODELS Min Min Doctor of Philosophy, 2007 Dissertation directed by: Professor Paul J. Smith Statistics Program Department of Mathematics Generalized Linear Mixed Models (GLMMs) extend the framework of Generalized Linear Models (GLMs) by including random effects into the linear predictor. This will achieve two main goals of ...