Statistical Inference

Produktbeschreibung

Casella and Berger's new edition builds the theoretical statistics from the first principals of probability theory. Thoroughly and completely, the authors start with the basics of probability and then move on to develop the theory of statistical inference using techniques, definitions, and statistical concepts. 

Inhaltsverzeichnis

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.