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May 2012 Inference on power law spatial trends
Peter M. Robinson
Bernoulli 18(2): 644-677 (May 2012). DOI: 10.3150/10-BEJ349


Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space–time. Consistency and asymptotic normality of nonlinear least-squares estimates of the parameters are established. The joint limit distribution is singular, but can be used as a basis for inference on either exponents or coefficients. We discuss issues of implementation, efficiency, potential for improved estimation and possibilities of extension to more general or alternative trending models to allow for irregularly spaced data or heteroscedastic errors; though it focusses on a particular model to fix ideas, the paper can be viewed as offering machinery useful in developing inference for a variety of models in which power law trends are a component. Indeed, the paper also makes a contribution that is potentially relevant to many other statistical models: Our problem is one of many in which consistency of a vector of parameter estimates (which converge at different rates) cannot be established by the usual techniques for coping with implicitly-defined extremum estimates, but requires a more delicate treatment; we present a generic consistency result.


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Peter M. Robinson. "Inference on power law spatial trends." Bernoulli 18 (2) 644 - 677, May 2012.


Published: May 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1238.62106
MathSciNet: MR2922465
Digital Object Identifier: 10.3150/10-BEJ349

Keywords: asymptotic normality , consistency , Correlation , generalized polynomial , lattice , power law

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability


Vol.18 • No. 2 • May 2012
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