In this course, we study basics of probability theory and mathematical statistics. In addition, we study linear regression models, their nonlinear extension, and nonparametric methods to be able to use appropriate statistical methods for data analysis.
This course aims to grasp the idea of well-known statistical methods and master those methods.
independence of random variables, conditional probability, Bayes' formula, univariate and multivariate probability distributions, moment generating function, characteristic function, low of large numbers, central limit theorem, Slutsky' theorem, delta method, maximum likelihood estimator, confidence interval, linear regression, panel analysis, nonparametric method.
|✔ Specialist skills||Intercultural skills||Communication skills||✔ Critical thinking skills||✔ Practical and/or problem-solving skills|
We first study basic probability distributions which is often used in econometrics and statistics (classes 1-4). Then we study basic probability theory and asymptotic theory (classes 5-10). We introduce linear regression models and study asymptotic properties of least square estimators (classes 11-12). As extension of linear models, we also introduce some nonlinear regression other linear models models such as panel analysis and study those statistical properties (class 13). In class 14, we focus on nonparametric kernel method which are also often used in econometrics and statistics.
|Course schedule||Required learning|
|Class 1||Overview of this course.||Understand the purpose of this course.|
|Class 2||Random variables and those properties.||Understand the definition of random variables and those properties.|
|Class 3||Univariate probability distributions.||Understand univariate probability distributions.|
|Class 4||Multivariate probability distributions.||Understand multivariate probability distributions.|
|Class 5||Moment generating function and characteristic function.||Understand moment generating function and characteristic function.|
|Class 6||Law of large numbers.||Understand law of large numbers.|
|Class 7||Applications of law of large numbers.||Understand applications of law of large numbers.|
|Class 8||Central limit theorems.||Understand central limit theorems.|
|Class 9||Applications of central limit theorems.||Understand applications of central limit theorems.|
|Class 10||Maximum likelihood estimator and related topics.||Understand maximum likelihood estimator and related topics.|
|Class 11||Consistency of least square estimators.||Understand asymptotic normality of least square estimators.|
|Class 12||Asymptotic normality of least square estimators.||Understand simple econometric models.|
|Class 13||Asymptotic properties of estimators for panel data analysis.||Understand panel data analysis.|
|Class 14||Definition and asymptotic properties of kernel density/ regression estimators.||Understand asymptotic properties of kernel density/regression estimators.|
A reading list covering fundamental studies for each topic will be available in class.
The final grade is determined based on (i) class attendance (35%) and (ii) final report (65%).
Precisely, students are required to submit pdf files of (i) mid term assignments to confirm the degree of comprehension (i) and (ii) solutions of some exercises as a final report via the OCW-i system.
To take this course, students should be proficient in pre-intermediate linear algebra, mathematical analysis, econometrics, and mathematical statistics.