文章基本信息

标题：Inference on Power Law Spatial Trends (Running Title: Power Law Trends)
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作者：Peter M Robinson
期刊名称：Distributional Analysis Publications
印刷版ISSN：1352-2469
出版年度：2011
卷号：2011
出版社：Suntory Toyota International Centres for Economics and Related Disciplines
摘要：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 irregularlyspaced data or heteroscedastic errors; though it focusses on a particular model to .x 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 implicitlydefined extremum estimates, but requires a more delicate treatment; we present a generic consistency result.
关键词：asymptotic normality; consistency; correlation; generalized polynomial;lattice; power law.