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Introduction to mathematical statistics / Fetsje Bijma, Marianne Jonker, Aad van der Vaart

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Publisher: Amsterdam : Amsterdam University Press, [2017]Description: Online RessourceISBN:
  • 9789048536115
  • 9462985103
  • 9789462985100
Uniform titles:
  • Inleiding in de statistiek
Subject(s): Additional physical formats: 9789462985100. | Erscheint auch als: An introduction to mathematical statistics. Druck-Ausgabe Amsterdam : Amsterdam University Press, 2017. xi, 368 SeitenDDC classification:
  • 519.5
RVK: RVK: QH 232LOC classification:
  • QA276
Online resources: Summary: 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 VaccineSummary: 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 SelectionSummary: 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. TablesSummary: 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 HypothesisSummary: C.1. Normal DistributionC.2. t-Distribution; C.3. Chi-Square Distribution; C.4. Binomial Distribution (n = 10); D. Answersto Exercises; IndexPPN: PPN: 1003049354Package identifier: Produktsigel: GBV-4-CommColl | ZDB-4-EBA | ZDB-4-NLEBK
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