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Inference on power law spatial trends

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  • Peter Robinson

    (Institute for Fiscal Studies and London School of Economics)

Abstract

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, and 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.

Suggested Citation

  • Peter Robinson, 2011. "Inference on power law spatial trends," CeMMAP working papers CWP09/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:09/11
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    File URL: http://cemmap.ifs.org.uk/wps/cwp0911.pdf
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    References listed on IDEAS

    as
    1. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
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