## Bernoulli

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

### Semiparametric topographical mixture models with symmetric errors

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

#### 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