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Table of Contents
Intro; Contents; Contributors; Symmetrizing k-nn and Mutual k-nn Smoothers; 1 Introduction; 1.1 The Statistical Background; 1.2 k-nn and Mutual k-nn Smoothers; 1.3 Admissibility; 1.4 Symmetrization; 2 Symmetrization Procedures for Row-Stochastic Smoothers; 2.1 Geometric and Arithmetic Mean; 2.2 Cohen's and Zhao's Symmetrization; 3 Symmetrization of k-nn-Type Smoothers; 3.1 Construction of the Symmetrized Estimator; 3.2 Interpretation, Estimation at Any Point x; 4 Conclusion; Appendix; References; Nonparametric PU Learning of State Estimation in Markov Switching Model; 1 Introduction
4 Numerical Examples4.1 Local Study; 4.2 Global Study; 5 Conclusion; 6 Proofs; 6.1 Proof of Proposition 1; 6.2 Proof of Lemma 1; 6.3 Proof of Theorem 1; 6.4 Proof of Theorem 2; References; Efficiency of the V-Fold Model Selection for Localized Bases; 1 Introduction; 2 Model Selection Setting; 3 V-Fold Cross-Validation; 4 V-Fold Penalization; 5 Simulation Study; 6 Proofs; References; Non-parametric Lower Bounds and Information Functions; 1 Introduction; 2 Regularity Conditions and Lower Bounds; 3 Lower Bounds Based on Continuity Moduli; 4 On Unbiased Estimation; 5 On Consistent Estimation
6 On Uniform ConvergenceReferences; Modification of Moment-Based Tail Index Estimator: Sums Versus Maxima; 1 Introduction and Main Results; 2 Comparison; 3 Proofs; References; Constructing Confidence Sets for the Matrix Completion Problem; 1 Introduction; 2 Notation, Assumptions, and Some Basic Results; 3 A Non-asymptotic Confidence Set for the Matrix Completion Problem; 4 Technical Lemmas; References; A Nonparametric Classification Algorithm Based on Optimized Templates; 1 Introduction; 2 Methods; 2.1 Optimization Criterion; 2.2 Optimizing Templates; 3 Results; 3.1 Description of the Data
3.2 Locating the Mouth: Initial Results3.3 Optimal Mouth Template; 4 Discussion; 5 Conclusion; Reference; PAC-Bayesian Aggregation of Affine Estimators; 1 Introduction; 2 Framework and Estimate; 3 Penalization Strategies and Preliminary Results; 4 A General Oracle Inequality; References; Light- and Heavy-Tailed Density Estimation by Gamma-WeibullKernel; 1 Introduction; 1.1 Gamma Kernel; 2 Gamma-Weibull Kernel; 3 Convergence Rate of the Density Estimator; 3.1 The Optimal Bandwidth Parameters for the Density Estimator; 4 Conclusion; Appendix; Proof of Lemma 1; Proof of Lemma 2; References
4 Numerical Examples4.1 Local Study; 4.2 Global Study; 5 Conclusion; 6 Proofs; 6.1 Proof of Proposition 1; 6.2 Proof of Lemma 1; 6.3 Proof of Theorem 1; 6.4 Proof of Theorem 2; References; Efficiency of the V-Fold Model Selection for Localized Bases; 1 Introduction; 2 Model Selection Setting; 3 V-Fold Cross-Validation; 4 V-Fold Penalization; 5 Simulation Study; 6 Proofs; References; Non-parametric Lower Bounds and Information Functions; 1 Introduction; 2 Regularity Conditions and Lower Bounds; 3 Lower Bounds Based on Continuity Moduli; 4 On Unbiased Estimation; 5 On Consistent Estimation
6 On Uniform ConvergenceReferences; Modification of Moment-Based Tail Index Estimator: Sums Versus Maxima; 1 Introduction and Main Results; 2 Comparison; 3 Proofs; References; Constructing Confidence Sets for the Matrix Completion Problem; 1 Introduction; 2 Notation, Assumptions, and Some Basic Results; 3 A Non-asymptotic Confidence Set for the Matrix Completion Problem; 4 Technical Lemmas; References; A Nonparametric Classification Algorithm Based on Optimized Templates; 1 Introduction; 2 Methods; 2.1 Optimization Criterion; 2.2 Optimizing Templates; 3 Results; 3.1 Description of the Data
3.2 Locating the Mouth: Initial Results3.3 Optimal Mouth Template; 4 Discussion; 5 Conclusion; Reference; PAC-Bayesian Aggregation of Affine Estimators; 1 Introduction; 2 Framework and Estimate; 3 Penalization Strategies and Preliminary Results; 4 A General Oracle Inequality; References; Light- and Heavy-Tailed Density Estimation by Gamma-WeibullKernel; 1 Introduction; 1.1 Gamma Kernel; 2 Gamma-Weibull Kernel; 3 Convergence Rate of the Density Estimator; 3.1 The Optimal Bandwidth Parameters for the Density Estimator; 4 Conclusion; Appendix; Proof of Lemma 1; Proof of Lemma 2; References