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Cusp estimation in random design regression models
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Takayuki Fujii
Published/Copyright:
November 19, 2010
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
Published Online: 2010-11-19
Published in Print: 2009-12
© by Oldenbourg Wissenschaftsverlag, Tokyo, 190-8562, Germany
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Keywords for this article
cusp estimation;
likelihood ratio;
non-regular estimation;
Bayes estimator;
fractional Brownian motion
Articles in the same Issue
- A note on pivotal Value-at-Risk estimates
- A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets
- Cusp estimation in random design regression models
- On the mean residual waiting time of records
- A maximal inequality for skew Brownian motion
