Mathematical Statistics for Economics and Business /

This book is designed to provide beginning graduate stu­ dents and advanced undergraduates with a rigorous and accessible foundation in the principles of probability and mathematical statistics underlying statis­ tical inference in the fields of business and economics. The book assumes no prior know...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Mittelhammer, Ron (Ronald Carl), 1950- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York, 1996.
Temas:
Distribution (Probability theory)
Econometrics.
Mathematics.
Statistics.
Mathematics
Distribution (Théorie des probabilités)
Économétrie.
Mathématiques.
Statistique.
distribution (statistics-related concept)
statistics.
Econometrics
Statistics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Elements of Probability Theory
  • 1.1. Introduction
  • 1.2. Experiment, Sample Space, Outcome, and Event
  • 1.3. Nonaxiomatic Probability Definitions
  • 1.4. Axiomatic Definition of Probability
  • 1.5. Some Probability Theorems
  • 1.6. A Digression on Events
  • 1.7. Conditional Probability
  • 1.8. Independence
  • 1.9. Bayes's Rule
  • Key Words, Phrases, and Symbols
  • Problems
  • 2. Random Variables, Densities, and Cumulative Distribution Functions
  • 2.1. Introduction
  • 2.2. Univariate Random Variables and Density Functions
  • 2.3. Univariate Cumulative Distribution Functions
  • 2.4. Multivariate Random Variables, PDFs, and CDFs
  • 2.5. Marginal Probability Density Functions and CDFs
  • 2.6. Conditional Density Functions
  • 2.7. Independence of Random Variables
  • 2.8. Extended Example of Multivariate Concepts in the Continuous Case
  • 2.9. Events Occurring with Probability Zero
  • Key Words, Phrases, and Symbols
  • Problems
  • 3. Mathematical Expectation and Moments
  • 3.1. Expectation of a Random Variable
  • 3.2. Expectation of a Function of Random Variables
  • 3.3. Conditional Expectation
  • 3.4. Moments of a Random Variable
  • 3.5. Moment- and Cumulant-Generating Functions
  • 3.6. Joint Moments, Covariance, and Correlation
  • 3.7. Means and Variances of Linear Combinations of Random Variables
  • 3.8. Necessary and Sufficient Conditions for Positive Semidefiniteness
  • Key Words, Phrases, and Symbols
  • Problems
  • 4. Parametric Families of Density Functions
  • 4.1. Parametric Families of Discrete Density Functions
  • 4.2. Parametric Families of Continuous Density Functions
  • 4.3. The Normal Family of Densities
  • 4.4. The Exponential Class of Densities
  • Key Words, Phrases, and Symbols
  • Problems
  • 5. Basic Asymptotics
  • 5.1. Introduction
  • 5.2. Elements of Real Analysis
  • 5.3. Types of Random-Variable Convergence
  • 5.4. Laws of Large Numbers
  • 5.5. Central Limit Theorems
  • 5.6. Asymptotic Distributions of Differentiable Functions of Asymptotically Normally Distributed Random Variables
  • Key Words, Phrases, and Symbols
  • Problems
  • 6. Sampling, Sample Moments, Sampling Distributions, and Simulation
  • 6.1. Introduction
  • 6.2. Random Sampling
  • 6.3. Empirical or Sample Distribution Function
  • 6.4. Sample Moments and Sample Correlation
  • 6.5. Properties of X-n and S2n When Random Sampling from a Normal Distribution?
  • 6.6. Sampling Distributions: Deriving Probability Densities of Functions of Random Variables
  • 6.7. t-and F-Densities
  • 6.8. Random Sample Simulation and the Probability Integral Transformation
  • 6.9. Order Statistics
  • Key Words, Phrases, and Symbols
  • Problems
  • 7. Elements of Point Estimation Theory
  • 7.1. Introduction
  • 7.2. Statistical Models
  • 7.3. Estimators and Estimator Properties
  • 7.4. Sufficient Statistics
  • 7.5. Results on MVUE Estimation
  • Key Words, Phrases, and Symbols
  • Problems
  • 8. Point Estimation Methods
  • 8.1. Introduction
  • 8.2. Least Squares and the General Linear Model
  • 8.3. The Method of Maximum Likelihood
  • 8.4. The Method of Moments
  • Key Words, Phrases, and Symbols
  • Problems
  • 9. Elements of Hypothesis-Testing Theory
  • 9.1. Introduction
  • 9.2. Statistical Hypotheses
  • 9.3. Basic Hypothesis-Testing Concepts
  • 9.4. Parametric Hypothesis Tests and Test Properties
  • 9.5. Results on UMP Tests
  • 9.6. Noncentral t-Distribution
  • Key Words, Phrases, and Symbols
  • Problems
  • 10. Hypothesis-Testing Methods
  • 10.1. Introduction
  • 10.2. Heuristic Approach
  • 10.3. Generalized Likelihood Ratio Tests
  • 10.4. Lagrange Multiplier Tests
  • 10.5. Wald Tests
  • 10.6. Tests in the GLM
  • 10.7. Confidence Intervals and Regions
  • 10.8. Nonparametric Tests of Distributional Assumptions
  • 10.9. Noncentral?2
  • and P-Distributions
  • Key Words, Phrases, and Symbols
  • Problems
  • Appendix A. Math Review: Sets, Functions, Permutations, Combinations, and Notation
  • A.1. Introduction
  • A.2. Definitions, Axioms, Theorems, Corollaries, and Lemmas
  • A.3. Elements of Set Theory
  • Set-Defining Methods
  • Set Classifications
  • Special Sets, Set Operations, and Set Relationships
  • Rules Governing Set Operations
  • A.4. Relations, Point Functions, and Set Functions
  • Cartesian Product
  • Relation (Binary)
  • Function
  • Real-Valued Point Versus Set Functions
  • A.5. Combinations and Permutations
  • A.6. Summation, Integration and Matrix Differentiation Notation
  • Key Words, Phrases, and Symbols
  • Problems
  • Appendix B. Useful Tables
  • B.1. Cumulative Normal Distribution
  • B.2. Student's t Distribution
  • B.3. Chi-square Distribution
  • B.4. F-Distribution: 5% Points
  • B.5. F-Distribution: 1% Points.

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