| Description |
1 online resource |
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text file |
| Contents |
Cover; Table of Contents; 1. Introduction; 1.1. What Is Statistics?; 1.2. Statistical Models; Exercises; Application: Cox Regression; 2. Descriptive Statistics; 2.1. Introduction; 2.2. Univariate Samples; 2.3. Correlation; 2.4. Summary; Exercises; Application: Benford's Law; 3. Estimators; 3.1. Introduction; 3.2. Mean Square Error; 3.3. Maximum Likelihood Estimators; 3.4. Method of Moments Estimators; 3.5. Bayes Estimators; 3.6. M-Estimators; 3.7. Summary; Exercises; Application: Twin Studies; 4. Hypothesis Testing; 4.1. Introduction; 4.2. Null Hypothesis and Alternative Hypothesis. |
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4.3. Sample Size and Critical Region4.4. Testing with p-Values; 4.5. Statistical Significance; 4.6. Some Standard Tests; 4.7. Likelihood Ratio Tests; 4.8. Score and Wald Tests; 4.9. Multiple Testing; 4.10. Summary; Exercises; Application: Shares According to Black-Scholes; 5. Confidence Regions; 5.1. Introduction; 5.2. Interpretation of a Confidence Region; 5.3. Pivots and Near-Pivots; 5.4. Maximum Likelihood Estimators as Near-Pivots; 5.5. Confidence Regions and Tests; 5.6. Likelihood Ratio Regions; 5.7. Bayesian Confidence Regions; 5.8. Summary; Exercises; Application: The Salk Vaccine. |
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6. Optimality Theory6.1. Introduction; 6.2. Sufficient Statistics; 6.3. Estimation Theory; 6.4. Testing Theory; 6.5. Summary; Exercises; Application: High Water in Limburg; 7. Regression Models; 7.1. Introduction; 7.2. Linear Regression; 7.3. Analysis of Variance; 7.4. Nonlinear and Nonparametric Regression; 7.5. Classification; 7.6. Cox Regression Model; 7.7. Mixed Models; 7.8. Summary; Exercises; Application: Regression Models and Causality; 8. Model Selection; 8.1. Introduction; 8.2. Goal of Model Selection; 8.3. Test Methods; 8.4. Penalty Methods; 8.5. Bayesian Model Selection. |
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8.6. Cross-Validation8.7. Post-Model Selection Analysis; 8.8. Summary; Application: Air Pollution; A. Probability Theory; A.1. Introduction; A.2. Distributions; A.3. Expectation and Variance; A.4. Standard Distributions; A.5. Multivariate and Marginal Distributions; A.6. Independence and Conditioning; A.7. Limit Theorems and the Normal Approximation; Exercises; B. Multivariate Normal Distribution; B.1. Introduction; B.2. Covariance Matrices; B.3. Definition and Basic Properties; B.4. Conditional Distributions; B.5. Multivariate Central Limit Theorem; B.6. Derived Distributions; C. Tables. |
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C.1. Normal DistributionC. 2. t-Distribution; C.3. Chi-Square Distribution; C.4. Binomial Distribution (n = 10); D. Answersto Exercises; Index. |
| Summary |
The field of statistics focuses on drawing conclusions from data by modeling and analyzing the data using probabilistic models. The authors of this introductory text describe three key concepts from statistics--estimators, tests, and confidence regions--which they demonstrate and apply in an extensive variety of examples and case studies. An entire chapter covers regression models, including linear regression and analysis of variance. This book, designed for students, assumes a basic knowledge of probability theory, calculus, and linear algebra. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematical statistics -- Textbooks.
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Mathematical statistics. |
| Genre/Form |
Textbooks.
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Electronic books.
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Textbooks.
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| Other Form: |
Print version: Bijma, Fetsje. Introduction to mathematical statistics. Amsterdam, [Netherlands] : Amsterdam University Press, ©2017 xi, 368 pages 9789462985100 |
| ISBN |
9048536111 (electronic book) |
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9789048536115 (electronic book) |
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9462985103 |
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9789462985100 |
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