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Last edited on
Oct 17, 2024 by JJ.
Jan JOHANNES Oct 27,2023 Theses
Thesis:
Master in Mathematics

Author:
Holger Heck

Title:
Density estimation in a semiparametric convolution model

Supervisors:
Jan JOHANNES

Abstract:
In the following work we investigate a semiparametric additive noise model. We have given independent, identically distributed observations, each with the probability density p. This density consists of a convolution of an unknown density f and an exponentially smooth noise density. It is assumed that the noise density has an unknown self-similarity index, for which a consistent estimator will be presented. The estimated parameter is then used to estimate the unknown density f by a kernel method. We limit ourselves to polynomially smooth densities f of the Sobolev type. Furthermore, we will examine an estimator for the L2-norm of f and carry out a goodness-of-fit test.

Reference:
C. Butucea, C. Matias und C. Pouet. Adaptivity in convolution models with partially known noise distribution, Electronic Journal of Statistics, 2:897–915, 2008.