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May 2017 Semiparametric topographical mixture models with symmetric errors
C. Butucea, R. Ngueyep Tzoumpe, P. Vandekerkhove
Bernoulli 23(2): 825-862 (May 2017). DOI: 10.3150/15-BEJ760


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.


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C. Butucea. R. Ngueyep Tzoumpe. P. Vandekerkhove. "Semiparametric topographical mixture models with symmetric errors." Bernoulli 23 (2) 825 - 862, May 2017.


Received: 1 December 2014; Revised: 1 August 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 1384.62211
MathSciNet: MR3606752
Digital Object Identifier: 10.3150/15-BEJ760

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability


Vol.23 • No. 2 • May 2017
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