Lectures on Empirical Processes
Theory and Statistical Applications
Paul Deheuvels
Université de Paris VI, FranceEustasio del Barrio
Universidad de Valladolid, SpainSara van de Geer
ETH Zürich, Switzerland
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| FrontmatterDownload pp. i–iv | |
| PrefaceDownload pp. v–vi | |
| ContentsDownload pp. vii–ix | |
| Empirical and Quantile Processes in the Asymptotic Theory of Goodness-of-fit Testsp. 1 | |
| 1 | Introductionpp. 1–2 |
| 2 | Testing fit to a fixed distributionpp. 2–12 |
| 3 | Some tools from empirical processes theorypp. 12–30 |
| 4 | Testing fit to a family of distributionspp. 30–44 |
| 5 | Tests based on Wasserstein distancepp. 44–48 |
| 6 | Asymptotics for L2-functionals of the quantile processpp. 49–86 |
| Referencespp. 87–92 | |
| Topics on Empirical Processesp. 93 | |
| 1 | Introduction, notation and preliminariespp. 93–113 |
| 2 | Fluctuations of partial sumspp. 114–136 |
| 3 | Empirical processespp. 136–163 |
| 4 | Auxiliary resultspp. 164–180 |
| Referencespp. 180–190 | |
| Oracle Inequalities and Regularizationp. 191 | |
| 1 | Statistical modelspp. 191–200 |
| 2 | M-estimatorspp. 200–208 |
| 3 | The sequence space formulationpp. 209–221 |
| 4 | Overruling the variancepp. 221–229 |
| 5 | The -penaltypp. 229–241 |
| 6 | Tools from empirical process theorypp. 242–250 |
| Referencespp. 250–252 | |
| Indexpp. 253–254 |