Cusp estimation in random design regression models

Fujii Takayuki

Statistics & Risk Modeling, 2009, vol. 27, issue 3, 235-248

Abstract: We consider the parametric estimation for the random design nonlinear regression model whose regression function has an unknown cusp location. The Fisher information of this location parameter is unbounded, that is caused by the non-differentiability of the likelihood function, so this is a non-regular estimation problem. In this paper, we verify the asymptotic properties of the Bayes estimator (BE), e.g. the consistency, the asymptotic distribution and the convergence of its moments, by the likelihood ratio process whose limit is expressed in terms of fractional Brownian motion. Further, we show that the BE is asymptotically efficient in a certain minimax sense.

Keywords: cusp estimation; likelihood ratio; non-regular estimation; Bayes estimator; fractional Brownian motion (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:27:y:2009:i:3:p:235-248:n:1

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DOI: 10.1524/stnd.2009.1035

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