 Titel
An Introduction to Mathematical Statistics
Vertaler
Reinie Erné
Prijs
€ 34,99
ISBN
9789462985100
Uitvoering
Paperback
Aantal pagina's
384
Taal
Engels
Publicatiedatum
Afmetingen
17 x 24 cm
Ook beschikbaar als
eBook PDF - € 32,99
Inhoudsopgave
Toon inhoudsopgaveVerberg inhoudsopgave
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. WhatIsStatistics? . . . . . . . . . . . . . . . . . . . . . 1 1.2. StatisticalModels . . . . . . . . . . . . . . . . . . . . . 2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 12 Application: Cox Regression . . . . . . . . . . . . . . . . . 15 2. DescriptiveStatistics . . . . . . . . . . . . . . . . . . . . . . 21 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2. UnivariateSamples . . . . . . . . . . . . . . . . . . . . . 21 2.3. Correlation . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . 38 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 39 Application: Benford's Law . . . . . . . . . . . . . . . . . 41 3. Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2. MeanSquareError . . . . . . . . . . . . . . . . . . . . . 46 3.3. Maximum Likelihood Estimators . . . . . . . . . . . . . . . 54 3.4. MethodofMomentsEstimators . . . . . . . . . . . . . . . . 72 3.5. BayesEstimators . . . . . . . . . . . . . . . . . . . . . . 75 3.6. M-Estimators . . . . . . . . . . . . . . . . . . . . . . . 88 3.7. Summary . . . . . . . . . . . . . . . . . . . . . . . . . 93 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 94 Application: Twin Studies . . . . . . . . . . . . . . . . . 100 4. Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . 105 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 105 4.2. Null Hypothesis and Alternative Hypothesis . . . . . . . . . . 105 4.3. SampleSizeandCriticalRegion . . . . . . . . . . . . . . 107 4.4. Testing with p-Values . . . . . . . . . . . . . . . . . . . 121 4.5. StatisticalSignificance . . . . . . . . . . . . . . . . . . 126 4.6. SomeStandardTests . . . . . . . . . . . . . . . . . . . 127 4.7. Likelihood Ratio Tests . . . . . . . . . . . . . . . . . . 143 4.8. ScoreandWaldTests . . . . . . . . . . . . . . . . . . . 150 4.9. Multiple Testing . . . . . . . . . . . . . . . . . . . . . 153 4.10. Summary . . . . . . . . . . . . . . . . . . . . . . . . 159 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 160 Application: Shares According to Black-Scholes . . . . . . . . 169 5. ConfidenceRegions . . . . . . . . . . . . . . . . . . . . . 174 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 174 5.2. Interpretation of a Confidence Region . . . . . . . . . . . . 174 5.3. PivotsandNear-Pivots . . . . . . . . . . . . . . . . . . 177 5.4. Maximum Likelihood Estimators as Near-Pivots . . . . . . . . 181 5.5. ConfidenceRegionsandTests . . . . . . . . . . . . . . . 195 5.6. Likelihood Ratio Regions . . . . . . . . . . . . . . . . . 198 5.7. BayesianConfidenceRegions . . . . . . . . . . . . . . . . 201 5.8. Summary . . . . . . . . . . . . . . . . . . . . . . . . 205 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 206 Application: The Salk Vaccine . . . . . . . . . . . . . . . 209 6. Optimality Theory . . . . . . . . . . . . . . . . . . . . . . 212 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 212 6.2. SufficientStatistics . . . . . . . . . . . . . . . . . . . . 212 6.3. EstimationTheory . . . . . . . . . . . . . . . . . . . . 219 6.4. TestingTheory . . . . . . . . . . . . . . . . . . . . . 231 6.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . 245 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 246 Application: High Water in Limburg . . . . . . . . . . . . . 250 7. RegressionModels . . . . . . . . . . . . . . . . . . . . . . 259 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 259 7.2. LinearRegression . . . . . . . . . . . . . . . . . . . . 261 7.3. AnalysisofVariance . . . . . . . . . . . . . . . . . . . 275 7.4. Nonlinear and Nonparametric Regression . . . . . . . . . . . 283 7.5. Classification . . . . . . . . . . . . . . . . . . .

# An Introduction to Mathematical Statistics

De onderstaande tekst is niet beschikbaar in het Nederlands en wordt in het Engels weergegeven.
Statistics is the science that focuses on drawing conclusions from data, by modeling and analyzing the data using probabilistic models. In An Introduction to Mathematical Statistics the authors describe key concepts from statistics and give a mathematical basis for important statistical methods. Much attention is paid to the sound application of those methods to data.

The three main topics in statistics are estimators, tests, and confidence regions. The authors illustrate these in many examples, with a separate chapter on regression models, including linear regression and analysis of variance. They also discuss the optimality of estimators and tests, as well as the selection of the best-fitting model.

Each chapter ends with a case study in which the described statistical methods are applied. This book assumes a basic knowledge of probability theory, calculus, and linear algebra.