Martingale-coboundary representation for a class of random fields

Martingale–Coboundary Representation for a Class of Random Fields

Martingale approximation is one of methods of proving limit theorems for stationary random sequences. The method, in its simplest version, consists of representing the original random sequence as the sum of a martingale difference sequence and a coboundary sequence. In this introduction we give a brief sketch of this approach. The aim of the present paper is to extend the martingale approximati...

Random Projection-Based Anderson-Darling Test for Random Fields

In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R, and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior o...

A unifying representation for a class of dependent random measures

We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing dependent random measures can be seen as specific cases of this framework. In...

A Martingale Representation for Matching Estimators

A Martingale Representation for Matching Estimators Matching estimators are widely used in statistical data analysis. However, the distribution of matching estimators has been derived only for particular cases (Abadie and Imbens, 2006). This article establishes a martingale representation for matching estimators. This representation allows the use of martingale limit theorems to derive the asym...

The Erwin Schrr Odinger International Institute for Mathematical Physics Martingale-diierence Random Fields Limit Theorems and Some Applications Martingale-diierence Random Fields. Limit Theorems and Some Applications