All of Statistics: A Concise Course in Statistical Inference

Not a good one for getting started, very formal and less intuitive.

Useful.

NA

Indeholder "Preface", "Statistics /Data Mining Dictionary", "I. Probability", " 1. Probability", " 1.1 Introduction", " 1.2 Sample Spaces and Events", " 1.3 Probability", " 1.4 Probability on Finite Sample Spaces", " 1.5 Independent Events", " 1.6 Conditional Probability", " 1.7 Bayes' Theorem", " 1.8 Bibliographic Remarks", " 1.9 Appendix", " 1.10 Exercises", " 2. Random Variables", " 2.1 Introduction", " 2.2 Distribution Functions and Probability Functions", " 2.3 Some Important Discrete Random Variables", " 2.4 Some Important Continuous Random Variables", " 2.5 Bivariate Distributions", " 2.6 Marginal Distributions", " 2.7 Independent Random Variables", " 2.8 Conditional Distributions", " 2.9 Multivariate Distributions and lID show more Samples", " 2.10 Two Important Multivariate Distributions", " 2.11 Transformations of Random Variables", " 2.12 Transformations of Several Random Variables", " 2.13 Appendix", " 2.14 Exercises", " 3. Expectation", " 3.1 Expectation of a Random Variable", " 3.2 Properties of Expectations", " 3.3 Variance and Covariance", " 3.4 Expectation and Variance of Important Random Variables", " 3.5 Conditional Expectation", " 3.6 Moment Generating Functions", " 3.7 Appendix", " 3.8 Exercises", " 4. Inequalities", " 4.1 Probability Inequalities", " 4.2 Inequalities For Expectations", " 4.3 Bibliographic Remarks", " 4.4 Appendix", " 4.5 Exercises", " 5. Convergence of Random Variables", " 5.1 Introduction", " 5.2 Types of Convergence", " 5.3 The Law of Large Numbers", " 5.4 The Central Limit Theorem", " 5.5 The Delta Method", " 5.6 Bibliographic Remarks", " 5.7 Appendix", " 5.7.1 Almost Sure and L1 Convergence", " 5.7.2 Proof of the Central Limit Theorem", " 5.8 Exercises", "II. Statistical Inference", " 6. Models, Statistical Inference and Learning", " 6.1 Introduction", " 6.2 Parametric and Nonparametric Models", " 6.3 Fundamental Concepts in Inference", " 6.3.1 Point Estimation", " 6.3.2 Confidence Sets", " 6.3.3 Hypothesis Testing", " 6.4 Bibliographic Remarks", " 6.5 Appendix", " 6.6 Exercises", " 7. Estimating the CDF and Statistical Functionals", " 7.1 The Empirical Distribution Function", " 7.2 Statistical Fmctionals", " 7.3 Bibliographic Remarks", " 7.4 Exercises", " 8. The Bootstrap", " 8.1 Simulation", " 8.2 Bootstrap Variance Estimation", " 8.3 Bootstrap Confidence Intervals", " 8.4 Bibliographic Remarks", " 8.5 Appendix", " 8.5.1 The Jackknife", " 8.5.2 Justification For The Percentile Interval", " 8.6 Exercises", " 9. Parametric Inference", " 9.1 Parameter of Interest", " 9.2 The Method of Moments", " 9.3 Maximum Likelihood", " 9.4 Properties of Maximum Likelihood Estimators", " 9.5 Consistency of Maximum Likelihood Estimators", " 9.6 Equivariance of the MLE", " 9.7 Asymptotic Normality", " 9.8 Optimality", " 9.9 The Delta Method", " 9.10 Multiparameter Models", " 9.11 The Parametric Bootstrap", " 9.12 Checking Assumptions", " 9.13 Appendix", " 9.13.1 Proofs", " 9.13.2 Sufficiency", " 9.13.3 Exponential Families", " 9.13.4 Computing Maximum Likelihood Estimates", " 9.14 Exercises", " 10. Hypothesis Testing and p-values", " 10.1 The Wald Test", " 10.2 p-vaiues", " 10.3 The X2 Distribution", " 10.4 Pearson's X2 Test For Multinomial Data", " 10.5 The Permutation Test", " 10.6 The Likelihood Ratio Test", " 10.7 Multiple Testing", " 10.8 Goodness-of-fit Tests", " 10.9 Bibliographic Remarks", " 10.10 Appendix", " 10.10.1 The Neyman-Pearson Lemma", " 10.10.2 The t-test", " 10.11 Exercises", " 11. Bayesian Inference", " 11.1 The Bayesian Philosophy", " 11.2 The Bayesian Method", " 11.3 Functions of Parameters", " 11.4 Simulation", " 11.5 Large Sample Properties of Bayes' Procedures", " 11.6 Flat Priors, Improper Priors, and "Noninformative" Priors", " 11.7 Multiparameter Problems", " 11.8 Bayesian Testing", " 11.9 Strengths and Weaknesses of Bayesian Inference", " 11.10 Bibliographic Remarks", " 11.11 Appendix", " 11.12 Exercises", " 12. Statistical Decision Theory", " 12.1 Preliminaries", " 12.2 Comparing Risk Functions", " 12.3 Bayes Estimators", " 12.4 Minimax Rules", " 12.5 Maximum Likelihood, Minimax, and Bayes", " 12.6 Admissibility", " 12.7 Stein's Paradox", " 12.8 Bibliographic Remarks", " 12.9 Exercises", "III. Statistical Models and Methods", " 13. Linear and Logistic Regression", " 13.1 Simple Linear Regression", " 13.2 Least Squares and Maximum Likelihood", " 13.3 Properties of the Least Squares Estimators", " 13.4 Prediction", " 13.5 Multiple Regression", " 13.6 Model Selection", " 13.7 Logistic Regression", " 13.8 Bibliographic Remarks", " 13.9 Appendix", " 13.10 Exercises", " 14. Multivariate Models", " 14.1 Random Vectors", " 14.2 Estimating the Correlation", " 14.3 Multivariate Normal", " 14.4 Multinomial", " 14.5 Bibliographic Remarks", " 14.6 Appendix", " 14.7 Exercises", " 15. Inference About Independence", " 15.1 Two Binary Variables", " 15.2 Two Discrete Variables", " 15.3 Two Continuous Variables", " 15.4 One Continuous Variable and One Discrete", " 15.5 Appendix", " 15.6 Exercises", " 16. Causal Inference", " 16.1 The Counterfactual Model", " 16.2 Beyond Binary Treatments", " 16.3 Observational Studies and Confounding", " 16.4 Simpson's Paradox", " 16.5 Bibliographic Remarks", " 16.6 Exercises", " 17. Directed Graphs and Conditional Independence", " 17.1 Introduction", " 17.2 Conditional Independence", " 17.3 DAGs", " 17.4 Probability and DAGs", " 17.5 More Independence Relations", " 17.6 Estimation for DAGs", " 17.7 Bibliographic Remarks", " 17.8 Appendix", " 17.9 Exercises", " 18. Undirected Graphs", " 18.1 Undirected Graphs", " 18.2 Probability and Graphs", " 18.3 Cliques and Potentials", " 18.4 Fitting Graphs to Data", " 18.5 Bibliographic Remarks", " 18.6 Exercises", " 19. Log-Linear Models", " 19.1 The Log-Linear Model", " 19.2 Graphical Log-Linear Models", " 19.3 Hierarchical Log-Linear Models", " 19.4 Model Generators", " 19.5 Fitting Log-Linear Models to Data", " 19.6 Bibliographic Remarks", " 19.7 Exercises", " 20. Nonparametric Curve Estimation", " 20.1 The Bias-Variance Tradeoff", " 20.2 Histograms", " 20.3 Kernel Density Estimation", " 20.4 Nonparametric Regression", " 20.5 Appendix", " 20.6 Bibliographic Remarks", " 20.7 Exercises", " 21. Smoothing Using Orthogonal Functions", " 21.1 Orthogonal Functions and L2 Spaces", " 21.2 Density Estimation", " 21.3 Regression", " 21.4 Wavelets", " 21.5 Appendix", " 21.6 Bibliographic Remarks", " 21.7 Exercises", " 22. Classification", " 22.1 Introduction", " 22.2 Error Rates and the Bayes Classifier", " 22.3 Gaussian and Linear Classifiers", " 22.4 Linear Regression and Logistic Regression", " 22.5 Relationship Between Logistic Regression and LDA", " 22.6 Density Estimation and Naive Bayes", " 22.7 Trees", " 22.8 Assessing Error Rates and Choosing a Good Classifier", " 22.9 Support Vector Machines", " 22.10 Kernelization", " 22.11 Other Classifiers", " 22.12 Bibliographic Remarks", " 22.13 Exercises", " 23. Probability Redux: Stochastic Processes", " 23.1 Introduction", " 23.2 Markov Chains", " 23.3 Poisson Processes", " 23.4 Bibliographic Remarks", " 23.5 Exercises", " 24. Simulation Methods", " 24.1 Bayesian Inference Revisited", " 24.2 Basic Monte Carlo Integration", " 24.3 Importance Sampling", " 24.4 MCMC Part I: The Metropolis- Hastings Algorithm", " 24.5 MCMC Part II: Different Flavors", " 24.6 Bibliographic Remarks", " 24.7 Exercises", "Index".

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