Robinson, Peter M. (2011) Inference on power law spatial trends (Running Title: Power Law Trends). Econometrics (EM/2011/556). Suntory and Toyota International Centres for Economics and Related Disciplines, London, UK.
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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 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.J
| Item Type: | Monograph (Report) |
|---|---|
| Official URL: | http://sticerd.lse.ac.uk/ |
| Additional Information: | © 2011 The Authors |
| Divisions: | Economics STICERD |
| Subjects: | H Social Sciences > HB Economic Theory |
| Date Deposited: | 22 Jul 2014 10:31 |
| Last Modified: | 12 Dec 2024 05:56 |
| URI: | http://eprints.lse.ac.uk/id/eprint/58100 |
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