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| Nonparametric estimators | |
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| Examples of nonparametric models and problems | |
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| Kernel density estimators | |
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| Mean squared error of kernel estimators | |
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| Construction of a kernel of order l | |
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| Integrated squared risk of kernel estimators | |
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| Lack of asymptotic optimality for fixed density | |
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| Fourier analysis of kernel density estimators | |
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| Unbiased risk estimation. Cross-validation density estimators | |
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| Nonparametric regression. The Nadaraya-Watson estimator | |
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| Local polynomial estimators | |
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| Pointwise and integrated risk of local polynomial estimators | |
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| Convergence in the sup-norm | |
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| Projection estimators | |
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| Sobolev classes and ellipsoids | |
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| Integrated squared risk of projection estimators | |
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| Generalizations | |
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| Oracles | |
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| Unbiased risk estimation for regression | |
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| Three Gaussian models | |
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| Notes | |
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| Exercises | |
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| Lower bounds on the minimax risk | |
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| Introduction | |
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| A general reduction scheme | |
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| Lower bounds based on two hypotheses | |
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| Distances between probability measures | |
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| Inequalities for distances | |
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| Bounds based on distances | |
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| Lower bounds on the risk of regression estimators at a point | |
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| Lower bounds based on many hypotheses | |
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| Lower bounds in L[subscript 2] | |
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| Lower bounds in the sup-norm | |
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| Other tools for minimax lower bounds | |
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| Fano's lemma | |
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| Assouad's lemma | |
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| The van Trees inequality | |
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| The method of two fuzzy hypotheses | |
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| Lower bounds for estimators of a quadratic functional | |
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| Notes | |
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| Exercises | |
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| Asymptotic efficiency and adaptation | |
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| Pinsker's theorem | |
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| Linear minimax lemma | |
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| Proof of Pinsker's theorem | |
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| Upper bound on the risk | |
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| Lower bound on the minimax risk | |
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| Stein's phenomenon | |
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| Stein's shrinkage and the James-Stein estimator | |
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| Other shrinkage estimators | |
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| Superefficiency | |
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| Unbiased estimation of the risk | |
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| Oracle inequalities | |
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| Minimax adaptivity | |
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| Inadmissibility of the Pinsker estimator | |
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| Notes | |
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| Exercises | |
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| Appendix | |
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| Bibliography | |
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| Index | |