Nonparametric Density Estimation: The L1 View
The first systematic single-source examination of density estimates. It develops, from first principles, the ``natural'' theory for density estimation, L1, and shows why the classical L2 theory masks some fundamental properties of density estimates. Chapters comprehensively treat consistency, lower bounds for rates of convergence, rates of convergence in L1, the transformed kernel estimate, applications in discrimination, and estimators based on orthogonal series. All theorems are fully proven in rigorous, step-by-step detail. Additionally, the relevant recent literature is tied in with the more classic works of Parzen, Rosenblatt, and others.
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LOWER BOUNDS FOR RATES
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