Download Additional Topics on Testing and Bayesian Statistics

Course No.
Course title
:
:
Number of credits
Number of Lectures – Tutorials – Practical
Faculty Name
:
:
:
MPE 171
Quantitative Methods (Statistics and
Introduction to Econometrics)
4
46 – 6 – 4
Subir Sen
Course outline
The course is aimed at familiarising students with the understanding and application of
probability and mathematical-statistics concepts on which statistical and econometric analyses of
economic data are based. An understanding of probability theory and statistical inference is a key
a foundation to later courses in econometrics, and are also important for advanced micro and
macro-economic courses. Specific learning objectives includes stating, interpreting, and
assessing the assumptions required for appropriate use and interpretation of estimators and
estimation results; how to derive statistical properties of random variables, functions of random
variables, and functions of sample data; the characteristics of different probability distributions
and major advantages and limitations of using these distributions for statistical or econometric
models; and the basic properties of the least squares estimator in the general linear model (single
equation econometric models) context and an introduction to estimation issues that arise when
basic assumptions underlying the model are violated.
Emphasis is also given to learning by doing and hence part of the learning objectives will involve
use of the MINITAB and EXCEL spreadsheet packages. In the practical sessions, students will
be exposed to using these software(s) for summarising and plotting data, basic probability
theory, testing hypotheses, correlation analysis and regression. After completion of the course,
students are expected to use the concepts and techniques learned in assignments and term paper.
Evaluation Procedure



1 Term paper:
2 minor tests:
1 major test (end semester):
25%
30% (15% each)
45%
Details of course content and allotted time
Topic
Introduction
What is Statistics?
What is Econometrics?
Descriptive Statistics: (a) Data types; Tabular and
Graphical Methods of data grouping and display
(b) Numerical Measures of Data: Five Measures of
Central Tendency, Dispersion and useful measures of
Allotted time
(hours)
Lectures Tutorials Practical
4
0
2
Topic
Dispersion, Other Measures of location – percentiles and
quartiles; Measures of Distribution Shape
Probability Theory
Probability concepts, types and basic rules, Conditional
probability and independence, Bayes Theorem
Random Variables
Discrete and Continuous random variables; probability
mass function, probability density function; Expectation
of a random variable and some special expectations mean, variance, moment generating functions; Multiple
random variables: Joint probability distribution of
discrete and continuous variables, properties of multiple
variables, conditional distributions and expectations,
covariance and correlation
Special Distributions
The Binomial and related distributions, Poisson
distribution, Geometric & Hyper-geometric distributions;
Uniform distribution, Normal distribution, Exponential
distribution; Gamma, Chi-square and Beta distributions
Sampling & Statistical Inferences
Statistics and parameters, Types of sampling – nonrandom and random or probability sampling; Sampling
with and without replacement; Types of Probability
sampling – simple random sampling, stratified random
sampling, systematic sampling, cluster sampling;
Sampling distributions - t and F distributions; Student’s
Theorem; Ordered Statistics – Quantiles
Estimation
Point estimate, interval estimate; Properties of estimators
– unbiased, consistency, minimum variance, efficiency,
sufficiency; Estimation of model parameters – mean,
proportion, variance, difference of means, ratio of
variances
Hypothesis Testing:
Introduction to hypothesis testing procedure, simple and
composite hypothesis, Type I and type II errors and the
power function; Neyman-Pearson Theorem; Parametric
tests- t-test, χ2- test, F-test; ANOVA – one way & two
way; Non Parametric Tests – Sign test, Wilcoxon signed
rank Test; Mann-Whitney-Wilcoxon test, Kurskal- Wallis
Test; Measures of Association – rank correlation &
Kendall’s tau
Allotted time
(hours)
Lectures Tutorials Practical
2
1
1
4
1
2
6
1
1
8
1
0
6
0
0
8
1
0
Topic
Additional Topics on Testing and Bayesian Statistics
Sufficiency, likelihood ratio test, subjective probability
and simple Bayesian procedures
Introduction to Regression Analysis
Theoretical constructs and empirical observable;
inference problems in non-experimental sciences; uses of
econometric models; Specification of simple linear
regression model, least square method of estimation,
classical assumptions, general and confidence approach
to hypothesis testing.
Total
Allotted time
(hours)
Lectures Tutorials Practical
4
0
0
4
1
2
46
6
4
Suggested readings
Text Books:
1. Introduction to Mathematical Statistics, 6th Ed. R. V. Hogg, J W. McKean and A. T.
Craig, Prentice-Hall (2008).
2. Econometrics, 1st Ed. J Woolridge, Cengage / South-Western Thomson Learning (2009).
Supplementary Books:
1. Introduction to the Theory of Statistics, 3rd Ed. A. M. Mood, F. A. Graybill and D. C.
Boes, McGraw Hill (1974).
2. Basic Statistics, 2nd Ed. A. L. Nagar and R. K. Das, Oxford University Press (1997). (for
Basic Statistics Review)
3. Statistics for Business and Economics, 1st Ed. D. R. Anderson, D. J. Sweeney and T. A.
Williams, Cengage / South-Western Thomson Learning (2002). (for problems and
numerical examples)
4. Basic Econometrics, 4th Ed. D Gujarati, Tata McGraw Hill (2000)
The term paper involves the following tasks:
Stage 1: One page essay describing any economic or business problem; the context in which it
occurs, and application of statistical technique either to identify or to resolve the problem.
Stage 2: A two page outline of the statistical concept addressed / applied in the paper preferably
in own words. The reason why the particular technique is undertaken for the economic problem
identified. Five articles/ research works from referred journals that are relevant to your topic
should be read for and referred to in this assignment.
Stage 3: Turn in a paper consisting of 15-20 double spaced typed pages. Not more than 5 pages
may be used to review related literature. The rest of the term paper should be devoted to
developing an statistical / economic model (if so or the selected economic problem) selected in
Stage I. The assumptions, objectives and policy implications that can be derived from the model
should be clearly stated.
All term papers are to be presented in class. Presentations should be of about 15 to 20 minutes
per student.