In this course, we study linear regression models, their nonlinear extension, and nonparametric methods to be able to use appropriate statistical method for data analysis.
The purpose of this course is to grasp the idea of some well-known statistical methods and master those methods.
series estimator asymptotic theory, linear regression, nonlinear regression, nonparametric regression, series estimators.
✔ Specialist skills | ✔ Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
We first study basic asymptotic theory which is often used in econometrics and statistics (classes 1-4). Then we introduce linear regression models and study asymptotic properties of least square estimators (classes 5-7). As extension of linear models, we also introduce some nonlinear regression models such as LAD and quantile regression and study those statistical properties (classes 8-9). In classes 10-15, we focus on nonparametric method which are also often used in econometrics and statistics. In particular, we study nonparametric kernel regression (classes 10-12) and series estimators (classes 13-15).
Course schedule | Required learning | |
---|---|---|
Class 1 | Overview of this course. | Understand the purpose of this course. |
Class 2 | Introduction to probability theory. | Understand basic results in probability theory. |
Class 3 | Law of large numbers. | Understand law of large numbers. |
Class 4 | Central limit theorems. | Understand central limit theorems. |
Class 5 | Definition of linear regression models. | Understand linear regression models. |
Class 6 | Consistency of least square estimators. | Understand asymptotic normality of least square estimators. |
Class 7 | Asymptotic normality of least square estimators. | Understand simple econometric models. |
Class 8 | Asymptotic properties of LAD estimators. | Understand asymptotic properties of LAD estimators. |
Class 9 | Asymptotic properties of quantile regression estimators. | Understand asymptotic properties of quantile regression estimators. |
Class 10 | Definition of nonparametric regression models. | Understand the definition of nonparametric regression models. |
Class 11 | Asymptotic properties of kernel density estimators. | Understand asymptotic properties of kernel density estimators. |
Class 12 | Asymptotic properties of nonparametric kernel regression estimators. | Understand asymptotic properties of nonparametric kernel regression estimators. |
Class 13 | Definition of series estimators. | Understand series estimators for nonparametric models. |
Class 14 | Consistency of series estimators. | Understand consistency of series estimators. |
Class 15 | Asymptotic normality of series estimators. | Understand asymptotic normality of series estimators. |
None.
A reading list covering fundamental studies for each topic will be available in class.
The final grade is determined based on class attendance (50%) and final exam (50%)
To take this course, students should be proficient in pre-intermediate linear algebra, mathematical analysis, econometrics, and mathematical statistics.