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Cusp estimation in random design regression models

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  • Fujii Takayuki

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.

Suggested Citation

  • Fujii Takayuki, 2009. "Cusp estimation in random design regression models," Statistics & Risk Modeling, De Gruyter, vol. 27(3), pages 235-248, December.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:3:p:235-248:n:1
    DOI: 10.1524/stnd.2009.1035
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    References listed on IDEAS

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    1. S. Dachian, 2003. "Estimation of Cusp Location by Poisson Observations," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 1-14, January.
    2. Pflug, Georg, 1982. "A statistically important Gaussian Process," Stochastic Processes and their Applications, Elsevier, vol. 13(1), pages 45-57, July.
    3. Rao, B. L. S. Prakasa, 1985. "Asymptotic theory of least squares estimator in a nonregular nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 3(1), pages 15-18, February.
    4. Prakasa Rao, B. L. S., 2004. "Estimation of cusp in nonregular nonlinear regression models," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 243-251, February.
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