## Nonparametric Density Estimation: The L1 ViewThe 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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### Contents

INTRODUCTION | 1 |

CONSISTENCY | 12 |

LOWER BOUNDS FOR RATES | 35 |

Copyright | |

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### Common terms and phrases

Analysis Annals apply arbitrary Assume asymptotic called Chapter choice choose chosen compact support completely concludes the proof consider consistency constant continuous defined definition densities f density estimate depending derivatives distribution E(In equal error example exists fact factor finite fixed follows function given gives histogram estimate implies independent inequality interval kernel estimate least Lebesgue Lemma lim inf lim sup lower bound Mathematical measure method minimal minimax nonparametric normal obtain optimal orthogonal series parameter particular positive probability problem proof of Theorem proved random variables rate of convergence replaced respectively Riemann integrable sample satisfying sequence series estimate side smoothing Statistics Step sufficient surely term Theory transformed uniform uniformly University upper bound valid variation