Lehrinhalte
Denisity estimation (L1 error, kernel estimate, universal consistency, rate of convergence, data-dependent choice of parameters), regression estimation with fixed design (least squares estimates, application of empirical process theory), regression estimation with random design (local averaging, least squares estimates, universal consistency, optimal rate of convergence, data-dependent choice of parameters)
Literature
Devroye: A Course In Density Estimation.
Devroye, Lugosi: Combinatorial methods in density estimation.
Györfi, Kohler, Krzyzak, Walk: A distribution-free theory of nonparametric regression.
van de Geer: Empirical Processes in M-Estimation.
Voraussetzungen
Probability Theory, Mathematical Statistics
Denisity estimation (L1 error, kernel estimate, universal consistency, rate of convergence, data-dependent choice of parameters), regression estimation with fixed design (least squares estimates, application of empirical process theory), regression estimation with random design (local averaging, least squares estimates, universal consistency, optimal rate of convergence, data-dependent choice of parameters)
Literature
Devroye: A Course In Density Estimation.
Devroye, Lugosi: Combinatorial methods in density estimation.
Györfi, Kohler, Krzyzak, Walk: A distribution-free theory of nonparametric regression.
van de Geer: Empirical Processes in M-Estimation.
Voraussetzungen
Probability Theory, Mathematical Statistics
- Lehrende: Michael Kohler
Semester: ST 2021