Random fields are stochastic processes indexed by a multidimensional parameter. They possess some interesting properties, e.g. isotropy and the Markov property, and satisfy laws of large numbers and weak convergence theorems under fairly general conditions. As such, random fields provide a...

We consider an omnibus test for the correct speci…cation of the dynamics of a sequence fx (t)gt2Zd in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis....

This paper establishes the asymptotic normality of frequency polygons in the context of stationary strongly mixing random fields indexed by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb {Z}^d$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>d</mi> </msup> </math> </EquationSource> </InlineEquation>. Our method allows us to consider only minimal conditions on the width bins and provides a simple criterion on the mixing...</equationsource></equationsource></inlineequation>

We consider an omnibus test for the correct speci…cation of the dynamics of a sequence fx (t)gt2Zd in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis....

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form Xk=g(εk−s,s∈Zd), k∈Zd, where (εi)i∈Zd are iid random variables...

This paper reviews a number of conceptual issues pertaining to the implementation of an explicit "spatial" perspective in applied econometrics. It provides an overview of the motivation for including spatial effects in regression models, both from a theory-driven as well as from a data-driven...

Existing indices of residential segregation are based on a partition of the city in neighborhoods: given a spatial distribution of racial groups, the index measures different segregation levels for different partitions. I propose a spatial approach, which estimates segregation at the individual...