Bernoulli

  • Bernoulli
  • Volume 23, Number 2 (2017), 825-862.

Semiparametric topographical mixture models with symmetric errors

C. Butucea, R. Ngueyep Tzoumpe, and P. Vandekerkhove

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Abstract

Motivated by the analysis of a Positron Emission Tomography (PET) imaging data considered in Bowen et al. [Radiother. Oncol. 105 (2012) 41–48], we introduce a semiparametric topographical mixture model able to capture the characteristics of dichotomous shifted response-type experiments. We propose a pointwise estimation procedure of the proportion and location functions involved in our model. Our estimation procedure is only based on the symmetry of the local noise and does not require any finite moments on the errors (e.g., Cauchy-type errors). We establish under mild conditions minimax properties and asymptotic normality of our estimators. Moreover, Monte Carlo simulations are conducted to examine their finite sample performance. Finally, a statistical analysis of the PET imaging data in Bowen et al. is illustrated for the proposed method.

Article information

Source
Bernoulli, Volume 23, Number 2 (2017), 825-862.

Dates
Received: December 2014
Revised: August 2015
First available in Project Euclid: 4 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1486177385

Digital Object Identifier
doi:10.3150/15-BEJ760

Mathematical Reviews number (MathSciNet)
MR3606752

Zentralblatt MATH identifier
1384.62211

Keywords
asymptotic normality consistency contrast estimators finite mixture of regressions Fourier transform identifiability inverse problem mixture model semiparametric symmetric errors

Citation

Butucea, C.; Ngueyep Tzoumpe, R.; Vandekerkhove, P. Semiparametric topographical mixture models with symmetric errors. Bernoulli 23 (2017), no. 2, 825--862. doi:10.3150/15-BEJ760. https://projecteuclid.org/euclid.bj/1486177385


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