Topics in Minimax Inference of Nonparametric Functionals
STATS 314B, Spring 2016, Stanford University.
Lecture 1
Introduction
Lecture 2
Influence Functions- Heuristics
Lecture 3
Nonexistence of Higher Order Influence Functions
Lecture 4
Estimation of Quadratic Functionals- Upper Bounds
Lecture 5
The Haar Wavelet and Hölder Spaces
Lecture 6
Estimation of Quadratic Functionals- Lower Bounds
Lecture 7
Nonparametric Hypothesis Testing- The Minimax Separation Framework
Lecture 8
Goodness of Fit Tests in Density Models in L
2
Separation
Lecture 9
Adaptive Estimation of Quadratic Functionals- Lepski's Method and Upper Bound
Lecture 10
Adaptive Estimation of Quadratic Functionals- Constrained Risk Inequality and Lower Bound
Lecture 11
Honest Adaptive Confidence Sets in L
2
- Generic Constructions
Lecture 12
Honest Adaptive Confidence Sets in L
2
in Density Models- The Adaptation Region
Lecture 13
Multiresolution Analysis, Compactly Supported Wavelet Bases, Approximations in Besov Spaces.
Lecture 14
Testing Regularity in a Density Model
Lecture 15
Honest Adaptive Confidence Sets in L
2
in Density Models- The Complete Picture
Lecture 16
The Theory of Influnce Functions- First and Higher Order