Owen Empirical Likelihood

Erscheinungsjahr 2010
ISBN: 978-1-4200-3615-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 304 Seiten

Reihe: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It also facilitates incorporating side information, and it simplifies accounting for censored, truncated, or biased sampling.

One of the first books published on the subject, Empirical Likelihood offers an in-depth treatment of this method for constructing confidence regions and testing hypotheses. The author applies empirical likelihood to a range of problems, from those as simple as setting a confidence region for a univariate mean under IID sampling, to problems defined through smooth functions of means, regression models, generalized linear models, estimating equations, or kernel smooths, and to sampling with non-identically distributed data. Abundant figures offer visual reinforcement of the concepts and techniques. Examples from a variety of disciplines and detailed descriptions of algorithms-also posted on a companion Web site at-illustrate the methods in practice. Exercises help readers to understand and apply the methods.

The method of empirical likelihood is now attracting serious attention from researchers in econometrics and biostatistics, as well as from statisticians. This book is your opportunity to explore its foundations, its advantages, and its application to a myriad of practical problems.

Zielgruppe

Researchers and practitioners in statistics, econometrics, engineering, and biostatistics

Autoren/Hrsg.

Owen, Art B.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

EMPIRICAL LIKELIHOOD (EL)
Introduction
Empirical Distribution Function
Nonparametric Maximum Likelihood
Nonparametric Likelihood Ratios
Ties in the Data
Multinomial on the Sample
EL for a Univariate Mean
Coverage Accuracy
Power and Efficiency
Empirical versus Parametric Inferences
Computing the Empirical Likelihood
EL FOR RANDOM VECTORS
NPMLE for Random Vectors
EL for a Multivariate Mean
Fisher, Bartlett, and Bootstrap Calibration
Smooth Functions of Means
Estimating Equations
Transformation Invariance of EL
Using Side Information
Convex dual Problem
Unconstrained Dual Problem
Solving the Dual Problem
Euclidean Likelihood
Other Nonparametric Likelihoods
REGRESSION AND MODELING
Sampling Pairs
Fixed Regressors
Triangular Array ELT
Analysis of Variance
Variance Modeling
Nonlinear Least Squared
Generalized Linear Models
Generalized Projection Pursuit
Plastic pipe Data
Euclidean likelihood for Regression and ANOVA
SYMMETRY AND INDEPENDENCE
Testing Symmetry
Constraining to Symmetry
Approximate Symmetry
Symmetric Unimodal Distributions
Testing Independence
Constraining to Independence
Approximate Independence
Permutation Tests
IMPERFECTLY OBSERVED DATA
Biased Sampling
Truncation
Multiple Biased Samples
Censoring
CURVE ESTIMATION
Kernel Estimates
Bias and Variance
EL for Kernel Smooths
Blood Pressure Trajectories
Simultaneous Inference
Bands for the ECDF
Bands for the Quantile Function
DEPENDENT DATA
Reducing to Independence
Blockwise Empirical Likelihood
Hierarchical Data
Dual likelihood for Martingales
HYBRIDS AND CONNECTIONS
Parametric Models for Subsets of Data
Parametric Models for Components of the Data
Parametric Models for Data Ranges
Empirical Likelihood and Bayes
Bayesian Bootstrap
Nonparametric tilting Bootstrap
Weighted Likelihood Bootstrap
Bootstrap Likelihoods
Jackknifes
SOME PROOFS
Lemmas
Vector ELT
Triangular Array ELT
Multisample ELT
ALGORITHMS
Smooth Optimization
Simple Hypotheses
Composite Hypotheses
Overdetermined NPMLE
Constraints
Partial Derivatives
Nested Algorithms
Gradient Equations
Primal Problem
Sequential Linearization
Sequential Linearization and Estimating Equations
Semi-infinite Programming
Profiling Empirical Likelihoods
HIGHER ORDER ASYMPTOTICS
Bartlett Correction
Pseudo-Likelihood Theory
Signed Root Corrections
Least Favorable Families
Large Deviations