Univ. Heidelberg
Statistics Group   Institute of Applied Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Institute of Applied Mathematics Statistics of inverse problems Research Group
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Last edited on
Oct 18, 2021 by JJ
Bachelor in Mathematics

Lena Krienke

Calibrating data-driven estimators in presence of censoring

Sergio Brenner Miguel and Jan JOHANNES

In this bachelor thesis we focus on the nonparametric estimation of a density f of a positive real-valued random variable X in the multiplicative censoring model. Instead of observing the random variable X we take a look on the random variable Y which is the product of X and U, hence Y = XU, with U as a β(1,k)-distributed random variable and X and U are independent. We project the density f on a subspace which is the linear span of the first m functions of the Laguerre basis. The projected density fm is estimated by . Then we get assertions about the mean integrated squared error of the density f and the projected density regarding to the upper and lower bound. Since primarily depends on m we have to estimate this parameter by a data-driven estimator. Subsequently we accentuate the theoretical statements by a Monte-Carlo simulation and have a view on various factors like the effect of an increasing k and different sample sizes.

Belomestny, Comte and Genon-Catalot. Nonparametric Laguerre estimation in the multiplicative censoring model, Electronic Journal of Statistics, 10(2):3114–315, 2016.
Brunel, Comte and Genon-Catalot: Nonparametric density and survival function estimation in the multiplicative censoring model, Test 25(3):570–590, 2016.