Probability and Statistics for Economists 1st edition by Yongmiao Hong – Ebook PDF Instant Download/Delivery: 9813228830 , 9789813228832
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ISBN 10: 9813228830
ISBN 13: 9789813228832
Author: Yongmiao Hong
Probability and Statistics have been widely used in various fields of science, including economics. Like advanced calculus and linear algebra, probability and statistics are indispensable mathematical tools in economics. Statistical inference in economics, namely econometric analysis, plays a crucial methodological role in modern economics, particularly in empirical studies in economics.This textbook covers probability theory and statistical theory in a coherent framework that will be useful in graduate studies in economics, statistics and related fields. As a most important feature, this textbook emphasizes intuition, explanations and applications of probability and statistics from an economic perspective.
Probability and Statistics for Economists 1st Table of contents:
1. Introduction to Probability and Statistics
1.1 Quantitative Analysis in Economics
1.2 Fundamental Axioms of Statistical Analysis in Economics
1.3 Role of Statistics in Economics
1.4 Limitation of Statistical Analysis in Economics
1.5 Conclusion
EXERCISE 1
2. Foundation of Probability Theory
2.1 Random Experiments
2.2 Basic Concepts of Probability
2.3 Review of Set Theory
2.4 Fundamental Probability Laws
2.4.1 Interpretation of Probability
2.4.2 Basic Probability Laws
2.5 Methods of Counting
2.5.1 Permutations
2.5.2 Combinations
2.6 Conditional Probability
2.7 Bayes’ Theorem
2.8 Independence
2.9 Conclusion
EXERCISE 2
3. Random Variables and Univariate Probability Distributions
3.1 Random Variables
3.2 Cumulative Distribution Function
3.3 Discrete Random Variables
3.4 Continuous Random Variables
3.5 Functions of a Random Variable
3.5.1 The Discrete Case
3.5.2 The Continuous Case
3.6 Mathematical Expectations
3.7 Moments
3.8 Quantiles
3.9 Moment Generating Function
3.10 Characteristic Function
3.11 Conclusion
EXERCISE 3
4. Important Probability Distributions
4.1 Introduction
4.2 Discrete Probability Distributions
4.2.1 Bernoulli Distribution
4.2.2 Binomial Distribution
4.2.3 Negative Binomial Distribution
4.2.4 Geometric Distribution
4.2.5 Poisson Distribution
4.3 Continuous Probability Distributions
4.3.1 Uniform Distribution
4.3.2 Beta Distribution
4.3.3 Normal Distribution
4.3.4 Cauchy and Stable Distributions
4.3.5 Lognormal Distribution
4.3.6 Gamma and Generalized Gamma Distributions
4.3.7 Chi-Square Distribution
4.3.8 Exponential and Weibull Distributions
4.3.9 Double Exponential Distribution
4.4 Conclusion
EXERCISE 4
5. Multivariate Probability Distributions
5.1 Random Vectors and Joint Probability Distributions
5.1.1 The Discrete Case
5.1.2 The Continuous Case
5.2 Marginal Distributions
5.2.1 The Discrete Case
5.2.2 The Continuous Case
5.3 Conditional Distributions
5.3.1 The Discrete Case
5.3.2 The Continuous Case
5.4 Independence
5.5 Bivariate Transformation
5.6 Bivariate Normal Distribution
5.7 Expectations and Covariance
5.8 Joint Moment Generating Function
5.9 Implications of Independence on Expectations
5.9.1 Independence and Moment Generating Functions
5.9.2 Independence and Uncorrelatedness
5.10 Conditional Expectations
5.11 Conclusion
EXERCISE 5
6. Introduction to Sampling Theory
6.1 Population and Random Sample
6.2 The Sampling Distribution of the Sample Mean
6.3 The Sampling Distribution of the Sample Variance
6.4 Student’s t-Distribution
6.5 Snedecor’s F Distribution
6.6 Sufficient Statistics
6.7 Conclusion
EXERCISE 6
7. Convergences and Limit Theorems
7.1 Limits and Orders of Magnitude: A Review
7.2 Motivation for Convergence Concepts
7.3 Convergence in Quadratic Mean and Lp-Convergence
7.4 Convergence in Probability
7.5 Almost Sure Convergence
7.6 Convergence in Distribution
7.7 Central Limit Theorems
7.8 Conclusion
EXERCISE 7
8. Parameter Estimation and Evaluation
8.1 Population and Distribution Model
8.2 Maximum Likelihood Estimation
8.3 Asymptotic Properties of MLE
8.4 Method of Moments and Generalized Method of Moments
8.4.1 Method of Moments Estimation
8.4.2 Generalized Method of Moments Estimation
8.5 Asymptotic Properties of GMM
8.6 Mean Squared Error Criterion
8.7 Best Unbiased Estimators
8.8 Cramer-Rao Lower Bound — An Alternative Method
8.9 Conclusion
EXERCISE 8
9. Hypothesis Testing
9.1 Introduction to Hypothesis Testing
9.2 Neyman-Pearson Lemma
9.3 Wald Test
9.4 Lagrange Multiplier (LM) Test
9.5 Likelihood Ratio Test
9.6 Illustrative Examples
9.6.1 Hypothesis Testing under the Bernoulli Distribution
9.6.2 Hypothesis Testing under the Normal Distribution
9.7 Conclusion
EXERCISE 9
10. Classical Linear Regression
10.1 Classical Linear Regression Model
10.2 OLS Estimation
10.3 Goodness of Fit and Model Selection Criteria
10.4 Consistency and Efficiency of the OLS Estimator
10.5 Sampling Distribution of the OLS Estimator
10.6 Variance Estimator of the OLS Estimator
10.7 Hypothesis Testing
10.7.1 Student’s t-Test
10.7.2 F-Test
10.8 Applications and Important Examples
10.8.1 Testing for Joint Significance of All Explanatory Variables
10.8.2 Testing for Omitted Variables
10.8.3 Testing for Linear Restrictions
10.9 Generalized Least Squares (GLS) Estimation
10.10 Conclusion
EXERCISE 10
11. Conclusion
EXERCISE 11
Bibliography
Index
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