- Thesis:
- Bachelor in Mathematics
- Author:
- Andreas Hillebrand
- Title:
- Nonparametric density estimation for grouped data
- Supervisors:
- Sergio Brenner Miguel
- Jan JOHANNES
- Abstract:
- In this thesis, we consider the problem of estimating the density f of a real-valued random variable X, where each available observation is the sum of independent copies of X. We construct an estimator based on a branch of the logarithm of the empirical characteristic function. Then, an upper bound for its risk is proven and convergence rates over suitable classes of densities are derived. Afterwards, we show a lower bound on the minimax risk over one of these classes. This leads to a minimax optimal convergence rate, up to a logarithmic loss. Further, we illustrate some of our findings in a numerical study.
References: - C. Duval and J. Kappus. Nonparametric adaptive estimation for grouped data, Journal of Statistical Planning and Inference 182, 12–28, 2017.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |