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Lectures on Empirical Processes

Theory and Statistical Applications

  • Paul Deheuvels

    Université de Paris VI, France
  • Eustasio del Barrio

    Universidad de Valladolid, Spain
  • Sara van de Geer

    ETH Zürich, Switzerland
Lectures on Empirical Processes cover
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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
1Introductionpp. 1–2
2Testing fit to a fixed distributionpp. 2–12
3Some tools from empirical processes theorypp. 12–30
4Testing fit to a family of distributionspp. 30–44
5Tests based on Wasserstein distancepp. 44–48
6Asymptotics for L2-functionals of the quantile processpp. 49–86
Referencespp. 87–92
Topics on Empirical Processesp. 93
1Introduction, notation and preliminariespp. 93–113
2Fluctuations of partial sumspp. 114–136
3Empirical processespp. 136–163
4Auxiliary resultspp. 164–180
Referencespp. 180–190
Oracle Inequalities and Regularizationp. 191
1Statistical modelspp. 191–200
2M-estimatorspp. 200–208
3The sequence space formulationpp. 209–221
4Overruling the variancepp. 221–229
5The 1\ell_1-penaltypp. 229–241
6Tools from empirical process theorypp. 242–250
Referencespp. 250–252
Indexpp. 253–254