- Thesis:
- Bachelor in Mathematics
- Author:
- Marlena WEIDENAUER
- Title:
- Uniform convergence of model-assisted mean estimators for sampled functional data
- Supervisor:
- Jan JOHANNES
- Abstract:
- Survey sampling describes the process of selecting a sample of elements from a target population. The advantage of sampling is that we only need data for a smaller group of the population. The data of this sample is then used to derive desired characteristics with respect to the whole population. This approach is used for large data sets, where the purpose is to reduce the costs obtained by storage or for taking the survey. Survey sampling is a helpful and efficient possibility for estimating different simple statistical quantities of the data. In this thesis the main target is the mean function. Thus, we get familiar with the terms of probability sampling designs on which basis estimators for the mean are then constructed. In this context we introduce the Horvitz-Thompson estimator for the mean and extend it to a functional framework. We then consider a linear regression model that takes, in addition to the data, auxiliary information and develop an estimator for the mean curve under the present model. Under mild assumptions on the sampling design and on the model we prove that the model assisted mean estimator is uniformly consistent.
- References:
- H. Cardot, C. Goga, and P. Lardin. Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data, Electronic Journal of Statistics, 7:562-596, 2013.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |