Research Catalog

Title

Empirical likelihood / Art B. Owen.

Author

Owen, Art B.

Publication

Boca Raton, Fla. : Chapman & Hall/CRC, [2001], ©2001.

Items in the Library & Off-site

Holdings

Details

Description

xii, 304 pages : illustrations; 24 cm.

Series Statement

Monographs on statistics and applied probability ; 92

Uniform Title

Monographs on statistics and applied probability (Series) ; 92.

Subject

• Estimation theory
• Probabilities
• Mathematical statistics
• Probability
• Statistics as Topic
• Estimation, Théorie de l'
• Probabilités
• Statistique
• Schattingstheorie
• Waarschijnlijkheid (statistiek)

Bibliography (note)

• Includes bibliographical references (p. [273]-286) and index.

Contents

1. Introduction -- 1.1. Earthworm segments, skewness and kurtosis -- 1.2. Empirical likelihood, parametric likelihood, and the bootstrap -- 1.3. Bibliographic notes -- 2. Empirical likelihood -- 2.1. Nonparametric maximum likelihood -- 2.2. Nonparametric likelihood ratios -- 2.3. Ties in the data -- 2.4. Multinomial on the sample -- 2.5. EL for a univariate mean -- 2.6. Coverage accuracy -- 2.7. One-sided coverage levels -- 2.8. Power and efficiency -- 2.9. Computing EL for a univariate mean -- 2.10. Empirical discovery of parametric families -- 2.11. Bibliographic notes -- 3. EL for random vectors -- 3.1. NPMLE for IID vectors -- 3.2. EL for a multivariate mean -- 3.3. Fisher, Bartlett, and bootstrap calibration -- 3.4. Smooth functions of means -- 3.5. Estimating equations -- 3.6. EL for quantiles -- 3.7. Ties and quantiles -- 3.8. Likelihood-based estimating equations -- 3.9. Transformation invariance of EL -- 3.10. Side information -- 3.11. Sandwich estimator -- 3.12. Robust estimators -- 3.13. Robust likelihood -- 3.14. Computation and convex duality -- 3.15. Euclidean likelihood -- 3.16. Other nonparametric likelihoods -- 3.17. Bibliographic notes -- 4. Regression and modeling -- 4.1. Random predictors -- 4.2. Nonrandom predictors -- 4.3. Triangular array ELT -- 4.4. Analysis of variance -- 4.5. Variance modeling -- 4.6. Nonlinear least squares -- 4.7. Generalized linear models -- 4.8. Poisson regression -- 4.9. Calibration, prediction, and tolerance regions -- 4.10. Euclidean likelihood for regression and ANOVA -- 4.11. Bibliographic notes -- 5. Empirical likelihood and smoothing -- 5.1. Kernel estimates -- 5.2. Bias and variance -- 5.3. EL for kernel smooths -- 5.4. Blood pressure trajectories -- 5.5. Conditional quantiles -- 5.6. Simultaneous inference -- 5.7. An additive model -- 5.8. Bibliographic notes -- 6. Biased and incomplete samples -- 6.1. Biased sampling -- 6.2. Multiple biased samples -- 6.3. Truncation and censoring -- 6.4. NPMLE's for censored and truncated data -- 6.5. Product-limit estimators -- 6.6. EL for right censoring -- 6.7. Proportional hazards -- 6.8. Further empirical likelihood ratio results -- 6.9. Bibliographic notes -- 7. Bands for distributions -- 7.1. The ECDF -- 7.2. Exact calibration of ECDF bands -- 7.3. Asymptotics of bands -- 7.4. Bibliographic notes -- 8. Dependent data -- 8.1. Time series -- 8.2. Reducing to independence -- 8.3. Blockwise empirical likelihood -- 8.4. Spectral method -- 8.5. Finite populations -- 8.6. MELE's using side information -- 8.7. Sampling designs -- 8.8. Empirical likelihood ratios for finite populations -- 8.9. Other dependent data -- 8.10. Bibliographic notes -- 9. Hybrids and connections -- 9.1. Product of parametric and empirical likelihoods -- 9.2. Parametric conditional likelihood -- 9.3. Parametric models for data ranges -- 9.4. Empirical likelihood and Bayes -- 9.5. Bayesian bootstrap -- 9.6. Least favorable families and nonparametric tilting -- 9.7. Bootstrap likelihood -- 9.8. Bootstrapping from an NPMLE -- 9.9. Jackknives -- 9.10. Sieves -- 9.11. Bibliographic notes -- 10. Challenges for EL -- 10.1. Symmetry -- 10.2. Independence -- 10.3. Comparison to permutation tests -- 10.4. Convex hull condition -- 10.5. Inequality and qualitative constraints -- 10.6. Nonsmooth estimating equations -- 10.7. Adverse estimating equations and black boxes -- 10.8. Bibliographic notes -- 11. Some proofs -- 11.1. Lemmas -- 11.2. Univariate and Vector ELT -- 11.3. Triangular array ELT -- 11.4. Multi-sample ELT -- 11.5. Bibliographic notes -- 12. Algorithms -- 12.1. Statistical tasks -- 12.2. Smooth optimization -- 12.3. Estimating equation methods -- 12.4. Partial derivatives -- 12.5. Primal problem -- 12.6. Sequential linearization -- 12.7. Bibliographic notes -- 13. Higher order asymptotics -- 13.1. Bartlett correction -- 13.2. Bartlett correction and smooth functions of means -- 13.3. Pseudo-likelihood theory -- 13.4. Signed root corrections -- 13.5. Large deviations -- 13.6. Bibliographic notes. App. A.1. Order and stochastic order notation -- App. A.2. Parametric models -- App. A.3. Likelihood -- App. A.4. The bootstrap idea -- App. A.5. Bootstrap confidence intervals -- App. A.6. Better bootstrap confidence intervals -- App. A.7. Bibliographic notes.

ISBN

1584880716 (alk. paper)

LCCN

2001028680

OCLC

• ocm46793086
• SCSB-5245172

Owning Institutions

Columbia University Libraries