2002 StatisticalInference
- (Garthwaite et al., 2002) ⇒ Paul Garthwaite, Ian Jolliffe, Byron Jones. (2002). “Statistical Inference, 2nd edition." Oxford University Press. ISBN:0-19-857226-3
Subject Headings: Statistical Inference, Estimator, Maximum Likelihood Estimation, Hypothesis Testing, Interval Estimation, Bayesian Inference, Nonparametric Statistical Inference, Robust Statistical Inference, Generalized Linear Model, Point Estimation, Hypothesis Testing,
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Book overview
Adopting a broad view of statistical inference, the text concentrates on what various techniques do, with mathematical proof kept to a minimum. The approach is rigorous but accessible to final year undergraduates. Classical approaches to point estimation, hypothesis testing and interval estimation are all covered thoroughly with recent developments outlined. Separate chapters are devoted to Bayesian inference, to decision theory and to non-parametric and robust inference. The increasingly important topics of computationally intensive methods and generalized linear models are also included. In this edition, the material on recent developments has been updated, and additional exercises are included in most chapters.
Preface
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... The purpose of this book is to build theoretical statistics (as difference from mathematical statistics) from the first principles of probability theory. …
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1. Probability Theory.
Set Theory. Probability Theory. Conditional Probability and Independence. Random Variables. Distribution Functions. Density and Mass Functions. Exercises. Miscellanea.
2. Transformations and Expectations.
Distribution of Functions of a Random Variable. Expected Values. Moments and Moment Generating Functions. Differentiating Under an Integral Sign. Exercises. Miscellanea.
3. Common Families of Distributions.
Introductions. Discrete Distributions. Continuous Distributions. Exponential Families. Locations and Scale Families. Inequalities and Identities. Exercises. Miscellanea.
4. Multiple Random Variables.
Joint and Marginal Distributions. Conditional Distributions and Independence. Bivariate Transformations. Hierarchical Models and Mixture Distributions. Covariance and Correlation. Multivariate Distributions. Inequalities. Exercises. Miscellanea.
5. Properties of a Random Sample.
Basic Concepts of Random Samples. Sums of Random Variables from a Random Sample. Sampling for the Normal Distribution. Order Statistics. Convergence Concepts. Generating a Random Sample. Exercises. Miscellanea.
6. Principles of Data Reduction.
Introduction. The Sufficiency Principle. The Likelihood Principle. The Equivariance Principle. Exercises. Miscellanea.
7. Point Estimation.
Introduction. Methods of Finding Estimators. Methods of Evaluating Estimators. Exercises. Miscellanea.
8. Hypothesis Testing.
Introduction. Methods of Finding Tests. Methods of Evaluating Test. Exercises. Miscellanea.
9. Interval Estimation.
Introduction. Methods of Finding Interval Estimators. Methods of Evaluating Interval Estimators. Exercises. Miscellanea.
10. Asymptotic Evaluations.
Point Estimation. Robustness. Hypothesis Testing. Interval Estimation. Exercises. Miscellanea.
11. Analysis of Variance and Regression.
Introduction. One-way Analysis of Variance. Simple Linear Regression. Exercises. Miscellanea.
12. Regression Models.
Introduction. Regression with Errors in Variables. Logistic Regression. Robust Regression. Exercises. Miscellanea. Appendix. Computer Algebra. References.
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