Aslan, Berkan: The concept of energy in nonparametric statistics: Goodness-of-Fit problems and deconvolution. 2004
Inhalt
- Contents
- 1. Introduction
- 2. Introduction to statistical test theory
- 2.1 Terminology
- 2.2 Types of statistical hypotheses
- 2.3 Tests of hypotheses
- 2.4 Goodness-of-Fit tests
- 2.5 Two-sample GoF tests
- 3. An overview of some relevant GoF tests
- 3.1 Tests based on binning
- 3.2 Binning-free tests
- 3.3 Three region test
- 3.4 Multivariate normality tests
- 4. The quantity energy as a GoF test
- 4.1 The interaction energy of a system of charges
- 4.2 The Energy tests
- 4.3 Proof of the minimum property of φ
- 4.4 Some selected distance functions
- 4.5 The distribution of the Energy test statistic
- 4.6 Consistency
- 4.7 A link between φnm and the Bowman-Foster test statistic
- 4.8 Power study
- 5. Energy for the two-sample problem
- 5.1 Resampling methods
- 5.2 The two-sample Energy test
- 5.3 Competing tests
- 5.4 Power comparisons
- 5.5 An example from high energy physics
- 6. Deconvolution
- 7. Summary
- Bibliography