# Syllabus

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## Description

The course introduces statistical theory to prepare students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, building functional forms, regression algebra, Gauss-Markov optimality, finite-sample inference, consistency, asymptotic normality, heteroscedasticity, and autocorrelation.

## Prerequisites

The prerequisites for this course include Calculus (18.02) and permission of the instructor.

## Course Requirements

Each week there are two lectures and a recitation.

The problem sets will be due roughly every two weeks. The answer key to the problems in *Statistical Inference* will be available. It is important to do problems and to try and solve those problems without having seen the answers.

## Texts

### Part 1

The text, which will be followed closely, is:

Casella, George, and Roger Berger. *Statistical Inference*. 2^{nd} ed. Pacific Grove, CA: Thomson Learning, 2001. ISBN: 9780534243128.

This book covers all of the material in Part 1 and provides many problems for practice as well as excellent references.

### Part 2

Greene, William. *Econometric Analysis*. 5^{th} ed. Upper Saddle River, NJ: Prentice-Hall, 2002. ISBN: 9780130661890.

Errors in the 5^{th} edition may be found here.

You can also find the material in any standard text on regression.

## Grading

ACTIVITIES | PERCENTAGES |
---|---|

Problem sets | 40% (15% in Part 1 and 25% in Part 2) |

Midterm Part I | 35% |

Final exam | 25% |

## Recommended Citation

For any use or distribution of these materials, please cite as follows:

Victor Chernozhukov, course materials for 14.381 Statistical Method in Economics, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

## Course Outline

### Part I

A. Brief review of probability

B. Random samples and asymptotic methods

- Sampling and sums of random variables
- Laws of large numbers and central limit theorem

C. Statistical theory

- Point estimation
- Evaluation of estimators: Unbiasedness, sufficiency, consistency, and the Cramer-Rao theorem
- Hypothesis tests, Neyman Pearson lemma, and Likelihood Ratio and related tests
- Interval estimation

### Part II

D. Fundamentals of regression

- Regression in economics
- Best linear predictor
- Best linear approximation
- Conditional expectation function
- Building functional forms

E. Regression in finite samples

- Basic regression algebra
- Gauss-markov optimality
- Finite-sample inference under normality and non-normality

F. Regression in large samples

- Consistency
- Asymptotic normality
- Heteroscedasticity
- Autocorrelation

G. Special topics (if time permits.)