Introduction to mathematical statistics

Introduction to mathematical statistics

For courses in mathematical statistics. Comprehensive coverage of mathematical statistics - with a proven approach Introduction to Mathematical Statistics by Hogg, McKean, and Craig enhances student comprehension and retention with numerous, illustrative examples and exercises. Classical statistical...

Descripción completa

Detalles Bibliográficos
Otros Autores: Hogg, Robert V., author (author), McKean, Joseph W., 1944- author, Craig, Allen T. (Allen Thornton), 1905- author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Harlow, Essex : Pearson [2020]
Edición:Eighth edition, global edition
Materias:
Mathematical statistics.
Libros electrónicos.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009749236706719
Tabla de Contenidos:
  • Front Cover
  • Title Page
  • Copyright Page
  • Dedication Page
  • Contents
  • Preface
  • 1 Probability and Distributions
  • 1.1 Introduction
  • 1.2 Sets
  • 1.2.1 Review of Set Theory
  • 1.2.2 Set Functions
  • 1.3 The Probability Set Function
  • 1.3.1 Counting Rules
  • 1.3.2 Additional Properties of Probability
  • 1.4 Conditional Probability and Independence
  • 1.4.1 Independence
  • 1.4.2 Simulations
  • 1.5 Random Variables
  • 1.6 Discrete Random Variables
  • 1.6.1 Transformations
  • 1.7 Continuous Random Variables
  • 1.7.1 Quantiles
  • 1.7.2 Transformations
  • 1.7.3 Mixtures of Discrete and Continuous Type Distributions
  • 1.8 Expectation of a Random Variable
  • 1.8.1 R Computation for an Estimation of the Expected Gain
  • 1.9 Some Special Expectations
  • 1.10 Important Inequalities
  • 2 Multivariate Distributions
  • 2.1 Distributions of Two Random Variables
  • 2.1.1 Marginal Distributions
  • 2.1.2 Expectation
  • 2.2 Transformations: Bivariate Random Variables
  • 2.3 Conditional Distributions and Expectations
  • 2.4 Independent Random Variables
  • 2.5 The Correlation Coefficient
  • 2.6 Extension to Several Random Variables
  • 2.6.1 *Multivariate Variance-Covariance Matrix
  • 2.7 Transformations for Several Random Variables
  • 2.8 Linear Combinations of Random Variables
  • 3 Some Special Distributions
  • 3.1 The Binomial and Related Distributions
  • 3.1.1 Negative Binomial and Geometric Distributions
  • 3.1.2 Multinomial Distribution
  • 3.1.3 Hypergeometric Distribution
  • 3.2 The Poisson Distribution
  • 3.3 The Γ, χ2, and β Distributions
  • 3.3.1 The χ2-Distribution
  • 3.3.2 The β-Distribution
  • 3.4 The Normal Distribution
  • 3.4.1 *Contaminated Normals
  • 3.5 The Multivariate Normal Distribution
  • 3.5.1 Bivariate Normal Distribution
  • 3.5.2 *Multivariate Normal Distribution, General Case
  • 3.5.3 *Applications
  • t- and F-Distributions.
  • 3.6.1 The t-distribution
  • 3.6.2 The F-distribution
  • 3.6.3 Student's Theorem
  • 3.7 *Mixture Distributions
  • 4 Some Elementary Statistical Inferences
  • 4.1 Sampling and Statistics
  • 4.1.1 Point Estimators
  • 4.1.2 Histogram Estimates of Pmfs and Pdfs
  • 4.2 Confidence Intervals
  • 4.2.1 Confidence Intervals for Difference in Means
  • 4.2.2 Confidence Interval for Difference in Proportions
  • 4.3 *Confidence Intervals for Parameters of Discrete Distributions
  • 4.4 Order Statistics
  • 4.4.1 Quantiles
  • 4.4.2 Confidence Intervals for Quantiles
  • 4.5 Introduction to Hypothesis Testing
  • 4.6 Additional Comments About Statistical Tests
  • 4.6.1 Observed Significance Level, p-value
  • 4.7 Chi-Square Tests
  • 4.8 The Method of Monte Carlo
  • 4.8.1 Accept-Reject Generation Algorithm
  • 4.9 Bootstrap Procedures
  • 4.9.1 Percentile Bootstrap Confidence Intervals
  • 4.9.2 Bootstrap Testing Procedures
  • 4.10 *Tolerance Limits for Distributions
  • 5 Consistency and Limiting Distributions
  • 5.1 Convergence in Probability
  • 5.1.1 Sampling and Statistics
  • 5.2 Convergence in Distribution
  • 5.2.1 Bounded in Probability
  • 5.2.2 Δ-Method
  • 5.2.3 Moment Generating Function Technique
  • 5.3 Central Limit Theorem
  • 5.4 *Extensions to Multivariate Distributions
  • 6 Maximum Likelihood Methods
  • 6.1 Maximum Likelihood Estimation
  • 6.2 Rao-Cram´er Lower Bound and Efficiency
  • 6.3 Maximum Likelihood Tests
  • 6.4 Multiparameter Case: Estimation
  • 6.5 Multiparameter Case: Testing
  • 6.6 The EM Algorithm
  • 7 Sufficiency
  • 7.1 Measures of Quality of Estimators
  • 7.2 A Sufficient Statistic for a Parameter
  • 7.3 Properties of a Sufficient Statistic
  • 7.4 Completeness and Uniqueness
  • 7.5 The Exponential Class of Distributions
  • 7.6 Functions of a Parameter
  • 7.6.1 Bootstrap Standard Errors
  • 7.7 The Case of Several Parameters.
  • 7.8 Minimal Sufficiency and Ancillary Statistics
  • 7.9 Sufficiency, Completeness, and Independence
  • 8 Optimal Tests of Hypotheses
  • 8.1 Most Powerful Tests
  • 8.2 Uniformly Most Powerful Tests
  • 8.3 Likelihood Ratio Tests
  • 8.3.1 Likelihood Ratio Tests for Testing Means of Normal Distributions
  • 8.3.2 Likelihood Ratio Tests for Testing Variances of Normal Distributions
  • 8.4 *The Sequential Probability Ratio Test
  • 8.5 *Minimax and Classification Procedures
  • 8.5.1 Minimax Procedures
  • 8.5.2 Classification
  • 9 Inferences About Normal Linear Models
  • 9.1 Introduction
  • 9.2 One-Way ANOVA
  • 9.3 Noncentral χ2 and F-Distributions
  • 9.4 Multiple Comparisons
  • 9.5 Two-Way ANOVA
  • 9.5.1 Interaction Between Factors
  • 9.6 A Regression Problem
  • 9.6.1 Maximum Likelihood Estimates
  • 9.6.2 *Geometry of the Least Squares Fit
  • 9.7 A Test of Independence
  • 9.8 The Distributions of Certain Quadratic Forms
  • 9.9 The Independence of Certain Quadratic Forms
  • 10 Nonparametric and Robust Statistics
  • 10.1 Location Models
  • 10.2 Sample Median and the Sign Test
  • 10.2.1 Asymptotic Relative Efficiency
  • 10.2.2 Estimating Equations Based on the Sign Test
  • 10.2.3 Confidence Interval for the Median
  • 10.3 Signed-Rank Wilcoxon
  • 10.3.1 Asymptotic Relative Efficiency
  • 10.3.2 Estimating Equations Based on Signed-Rank Wilcoxon
  • 10.3.3 Confidence Interval for the Median
  • 10.3.4 Monte Carlo Investigation
  • 10.4 Mann-Whitney-Wilcoxon Procedure
  • 10.4.1 Asymptotic Relative Efficiency
  • 10.4.2 Estimating Equations Based on the Mann-Whitney- Wilcoxon
  • 10.4.3 Confidence Interval for the Shift Parameter Δ
  • 10.4.4 Monte Carlo Investigation of Power
  • 10.5 *General Rank Scores
  • 10.5.1 Efficacy
  • 10.5.2 Estimating Equations Based on General Scores
  • 10.5.3 Optimization: Best Estimates
  • 10.6 *Adaptive Procedures
  • 10.7 Simple Linear Model.
  • 10.8 Measures of Association
  • 10.8.1 Kendall's τ
  • 10.8.2 Spearman's Rho
  • 10.9 Robust Concepts
  • 10.9.1 Location Model
  • 10.9.2 Linear Model
  • 11 Bayesian Statistics
  • 11.1 Bayesian Procedures
  • 11.1.1 Prior and Posterior Distributions
  • 11.1.2 Bayesian Point Estimation
  • 11.1.3 Bayesian Interval Estimation
  • 11.1.4 Bayesian Testing Procedures
  • 11.1.5 Bayesian Sequential Procedures
  • 11.2 More Bayesian Terminology and Ideas
  • 11.3 Gibbs Sampler
  • 11.4 Modern Bayesian Methods
  • 11.4.1 Empirical Bayes
  • A Mathematical Comments
  • A.1 Regularity Conditions
  • A.2 Sequences
  • B R Primer
  • B.1 Basics
  • B.2 Probability Distributions
  • B.3 R Functions
  • B.4 Loops
  • B.5 Input and Output
  • B.6 Packages
  • C Lists of Common Distributions
  • D Tables of Distributions
  • E References
  • F Answers to Selected Exercises
  • Index
  • Back Cover.

Ejemplares similares