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Regression for randomly sampled spatial series: the trigonometric case

Published online by Cambridge University Press:  14 July 2016

David R. Brillinger
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Abstract

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j} are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient.

Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j} is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

Keywords

POINT PROCESSPROCESS WITH STATIONARY INCREMENTSNON-LINEAR REGRESSIONTRIGONOMETRIC REGRESSIONPERIODOGRAMRANDOM MEASUREHIDDEN PERIODICITIESARRAY DATABLUE
Type
Part 5—Random Fields and Point Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 275 - 289
Copyright
Copyright © 1986 Applied Probability Trust 

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