Managing local dependencies in asymptotic theory for maxima of stationary random fields

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Asymptotic theory for stationary processes

In the study of random processes, dependence is the rule rather than the exception. To facilitate the related statistical analysis, it is necessary to quantify the dependence between observations. In the talk I will briefly review the history of this fundamental problem. By interpreting random processes as physical systems, I will introduce physical and predictive dependence coefficients that q...

Asymptotic Theory for Linear-Chain Conditional Random Fields

In this theoretical paper we develop an asymptotic theory for Linear-Chain Conditional Random Fields (L-CRFs) and apply it to derive conditions under which the Maximum Likelihood Estimates (MLEs) of the model weights are strongly consistent. We first define L-CRFs for infinite sequences and analyze some of their basic properties. Then we establish conditions under which ergodicity of the observ...

Asymptotic Theory of Cepstral Random Fields by Tucker

Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the autocovarianc...

Local Maxima of a Random Algebraic Polynomial

We present a useful formula for the expected number of maxima of a normal process ξ(t) that occur below a levelu. In the derivation we assume chiefly that ξ(t), ξ(t), and ξ(t) have, with probability one, continuous 1 dimensional distributions and expected values of zero. The formula referred to above is then used to find the expected number of maxima below the level u for the random algebraic p...