- Thesis:
- Master in Mathematics
- Author:
- Bérénice ROBERT
- Title:
- Adaptive non-parametric estimation in a multiplicative censoring model with symmetric noise
- Supervisors:
- Sergio Brenner Miguel
- Jan JOHANNES
- Abstract:
- In this thesis we study the non-parametric estimation of the density and survival function in a multiplicative censoring model with symmetric noise. We construct a projection estimator of an appropriate auxiliary function, from which we deduce an estimator of the function of interest. The variance order of each risk bound in terms of mean integrated squared error was proved in Comte and Dion (2016) and can now be improved using recent results (see Comte and Genon-Catalot (2018)). A method selection in each case yields the best possible projection parameter among a finite set minimising the risk bounds by realising the bias-variance compromise. A rate of convergence can be computed if the regularity of the auxiliary function is specified and we show that this rate is minimax-optimal for any estimator of the density function. Both adaptive estimators are illustrated on simulated data.
- Reference:
- F. Comte and C. Dion. Nonparametric estimation in a multiplicative censoring model with symmetric noise, Journal of Nonparametric Statistics, 28(4):768–801, 2016.
- F. Comte and V. Genon-Catalot. Laguerre and Hermite bases for inverse problems, Journal of the Korean Statistical Society, 47(3):273–296, 2018.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |