Download Large (and Finite-) Sample Properties of Estimators

ECON 2XX Statistics and Data Analysis
Course Outline
Fall 2009-10
Instructor:
Office:
Email:
Office Hours:
Danish Lakhani
XX (Extn: XX)
[email protected]
To be assigned
Description
This course provides an elementary introduction to probability and
statistics. Topics include: basic probability models; combinatorics; random
variables; discrete and continuous probability distributions; statistical
estimation and testing; confidence intervals; and an introduction to linear
regression.
Goals
On successful completion students:
1.
2.
3.
Will able to grasp the basic probability theory and its applications in the
field of economics.
Will be able to take advance courses in econometrics stream which will
help them in applied work.
Will be introduced to Statistical Software such as Stata and R language.
Prerequisites
Calculus 1,
Text Book
DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA:
Addison-Wesley, 2002. ISBN: 0201524880.
Reference:
David S. Moore and George P. McCabe: Introduction to the Practice of Statistics,
fifth edition, W.H. Freeman and Company, New York, 2006
Lectures
Two lectures of 100 minutes. The course outline below refers to sections from the
textbook. Relevant sections of the textbook are included in your course reading package.
In addition detailed class lecture notes would be posted on the course website.
Grading
Assignments
Midterm
Project
Final
15%
30%
15%
40%
Assignments: Students will be assigned weekly assignments. The grading of assignment
is on submission only. So students are advised to work on their own while trying to solve
these assignments. Exams will be based on problems similar to assignments questions.
Exams: There will be one in written midterm and one written final exam.
Project: Students will be assigned a small project to apply the knowledge of the course
to a real data set. Students would be required to use Statistical software such as STATA,
SPSS or EVIEWS, to complete this exercise.
Detailed Course Outline
Sr.
No.
1
2
3
4
5
6
7
8
Topic
Readings
Lectures
Probability Introduction:
Set operators, properties of probability, finite sample
space, combinatorics, Multinomial Coefficients, Union
of Events, Matching Problem, Conditional Probability,
Independence of Events, Bayes Theorm
Random Variables and Distributions:
Random variables, Cumulative Distribution functions,
Marginal Distribution, Conditional Distribution and
Multivariate Distribution, Functions of Random
Variables, Linear Transformations of Random Vector
Expectations and Variance:
Markov inequality, Chebyshev's Inequality, Properties
of Expectation, Variance, Standard Deviation, Law of
Large Numbers, Median, Covariance and Correlation,
Cauchy-Schwartz Inequality
MIDTERM
Distributions:
Poisson Distribution, Approximation of Binomial
Distribution, Normal Distribution, Normal
Distribution, Central Limit Theorem, Gamma
Distribution, Beta Distribution
Introduction to STATA**:
Lab session to introduce students to basics of the
software.
Estimation Theory:
Bayes' Estimators, Maximum Likelihood Estimators,
Chi-square Distribution, t-distribution, Confidence
Intervals for Parameters of Normal Distribution
Hypothesis testing:
Hypotheses Testing, Bayes' Decision Rules, t-test,
Two-sample t-test, Goodness-of-fit Tests, Pearson's
Theorem, Composite Hypotheses
Review
1.2-1.10, 2.12.3
1-3
3.1-3.10,
4-8
4.1-4.8,
5.2, 5.4, 5.6,
5.7, 5.9, 5.10
9-13
6.2-6.5, 7.2-7.5
14
15-20
21
8.2, 8.5, 8.6
22-26
9.1-9.4, 9.6
25-27
Lecture notes
28
*After the first three classes students would be introduced to R language software to do
basic exercises in probability and Stats.
**Class session would be devoted to introduce students to basics of a Statistical
Software.