Nonparametric Functional Estimation

PrefaceList of Notation1. Estimation of Functional 1.0. Introduction 1.1. Estimability of Functionals 1.2. Necessary and Sufficient Conditions for the Existence of Unbiased Estimators of Functionals 1.3. Asymptotic Efficiency of Estimators of Functionals Bibliographical Notes Problems2. Density Estimation (Univariate Case) 2.0. Introduction 2.1. The Method of Kernels 2.2. The Method of Orthogonal Series 2.3. The Method of Histograms with Fixed Partition 2.4. The Method of Histograms with Random Partition 2.5. The Method of Histosplines 2.6. The Method of Penalty Functions 2.7. The Method of Fourier Inversion 2.8. The Method of Delta Sequences 2.9. A Bayesian Approach 2.10. Comparison of Different Methods 2.11. Optimal Density Estimation 2.12. Invariant Density Estimation Bibliographical Notes Problems3. Density Estimation (Multivariate Case) 3.0. Introduction 3.1. The Method of Kernels 3.2. The Method of Nearest Neighbors 3.3. The Method of Orthogonal Series 3.4. The Method of Delta Sequence 3.5. The Method of Stochastic Approximation 3.6. Further Topics Bibliographical Notes Problems4. Estimation of Functionals Related to Density 4.0. Introduction 4.1. Estimation of Derivatives of a Density 4.2. Estimation of Regression Function 4.3. Estimation of Failure Rate 4.4. Estimation of Functionals of Density and Its Derivatives 4.5. Estimation of Mode 4.6. Further Topics Bibliographical Notes Problems5. Sequential and Recursive Estimation 5.0. Introduction 5.1. Recursive Estimation 5.2. Sequential Estimation Bibliographical Notes Problems6. Estimation for Stochastic Processes 6.1. Discrete Time Stationary Markov Processes 6.2. Discrete Time Stationary φ-Mixing Processes 6.3. Continuous Time Stationary Markov Processes 6.4. Diffusion Processes Bibliographical Notes Problems7. Estimation Under Order Restrictions 7.0. Introduction 7.1. Estimation of Unimodal Density 7.2. Estimation for Distributions with Monotone Failure Rates 7.3. Further Topics Bibliographical Notes Problems8. Nonparametric Discrimination 8.0. Introduction 8.1. Bayes Risk Consistency 8.2. Nearest Neighbor Rules 8.3. Histogram Method for Classification Bibliographical Notes Problems9. Estimation of a Distribution Function 9.0. Introduction 9.1. Estimation by the Method of Rao-Blackwellization 9.2. Estimation by the Method of Kernels 9.3. Estimation by the Method of Stochastic Approximation 9.4. Estimation of a Distribution Function from Incomplete Observations (Univariate Case) 9.5. Estimation in the Competing Risks Problem 9.6. Estimation of a Distribution Function from Incomplete Observations (Bivariate Case) Bibliographical Notes Problems10. Estimation of a Mixing Distribution 10.0. Introduction 10.1. Estimation for Finite Mixtures 10.2. Estimation for Arbitrary Mixtures Bibliographical Notes Problems11. Bayes Estimation 11.0. Introduction 11.1. Estimation of a Distribution Function 11.2. Estimation of a Distribution Function from Incomplete Data 11.3. Estimation of a Symmetric Distribution Function 11.4. Estimation of a Functional of a Distribution Function Bibliographical Notes ProblemsReferencesAuthor IndexSubject Index