Introduction to Statistics and Econometrics

1.1 General methodology of modern economic research

1.2 Roles of Econometrics

1.3 Illustrative Examples

1.4 Roles of Probability and Statistics

Quiz1

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

2.5 Methods of Counting

2.6 Conditional Probability

2.7 Bayes' Theorem

2.8 Independence

2.9 Conclusion

Quiz2

Random Variables and Univariate Probability Distributions

3.1 Random Variables

3.2 Cumulative Distribution Function

3.3 Discrete Random Variables(DRV)

3.4 Continuous Random Variables

3.5 Functions of a Random Variable

3.6 Mathematical Expectation

3.7 Moments

3.8 Quantiles

3.9 Moment Generating Function (MGF)

3.10 Characteristic Function

3.11 Conclusion

Quiz 3

Important Probability Distributions

4.1 Introduction

4.2 Discrete Probability Distributions

4.3 Continuous Probability Distributions

4.4 Conclusion

Quiz 4

Multivariate Probability Distributions

5.6 Bivariate Normal Distribution

5.7 Expectations and Covariance

5.8 Joint Moment Generating Function

5.9 Implications of Independence on Expectations

5.10 Conditional Expectations

5.11 Conclusion

5.1 Random Vectors and Joint Probability Distributions

5.2 Marginal Distributions

5.3 Conditional Distributions

5.4 Independence

5.5 Bivariate Transformation

Quiz 5

Introduction to Statistic

6.0 Introduction to Statistic

6.1 Population and Random Sample

6.2 Sampling Distribution of Sample Mean

6.3 Sampling Distribution of Sample Variance

6.4 Student’s t-Distribution_batch

6.5 Snedecor's F Distribution_batch

6.6 Sufficient Statistics

6.7 Conclusion_batch

Quiz 6

Chapter 7

7.0 Introduction

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_batch

Quiz 7

Chapter 8

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

8.5 Asymptotic Properties of GMM-zhong

8.6 Mean Squared Error Criterion

8.7 Best Unbiased Estimators

8.8 Cramer-Rao Lower Bound

Quiz 8

Chaper 9

9.1 Introduction to Hypothesis Testing

9.2 Neyman-Pearson Lemma-zhong

9.3 Wald Test_zhong

9.4 Lagrangian Multiplier (LM) Test

9.5 Likelihood Ratio Test

9.6 Illustrative Examples

Quiz 9

Chapter 10

10.1 Introduction

10.2 Empirical Studies and Statistical Inference

10.3 Important Features of Big Data

10.4 Big Data Analysis and Statistics