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Inference on power law spatial trends

Robinson, Peter M. (2012) Inference on power law spatial trends. Bernoulli, 18 (2). pp. 644-677. ISSN 1350-7265

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Identification Number: 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.

Item Type: Article
Official URL:
Additional Information: © 2012 International Statistical Institute/Bernoulli Society for Mathematical Statistics and Probability
Divisions: Economics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 25 Feb 2013 12:57
Last Modified: 20 Aug 2021 00:53

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