Statistical inference-I (STAT-6212)

Introduction

Statistical inference is the process of drawing inferences about population parameters on the basis of information obtained from sample drawn from population. This subject allow readers to make generalizations to a large number of individuals based on information from a limited number of objects.This subject is based on main three pillars of statistics i.e. Probability theory, sampling distributions statistical inference. There are many modes of performing inference including statistical modeling, data oriented strategies and involvment of designs and randomization in analyses. A practitioner can often be left in a debilitating maze of techniques, philosophies and nuance. This course presents the fundamentals of inference in a practical approach for getting things done. The main objective of this course is to provide a strong mathematical and conceptual foundation in the methods of statistical inference, with an emphasis on practical aspects of the interpretation and communication of statistically based conclusions in research. Statistical estimation is concerned with the best estimating a value or range of values for a particular population parameter. It deals with the estimation of parameters, properties of good point estimator and its methods. It also discusses the parameter estimation of different probability distributions and their efficiency. Bayesian Statistics and its comparison with classical estimation approach are part of the content.

Table of Contents

Estimation of parameters
Main points of estimation
Properties of good point estimators
Unbiasedness
consistency
Efficiency
Sufficiency
completeness
Cramer Rao Inequality
Lehmann-Scheffe Theorem
Rao-Black well theorem
Methods of estimation
Moments
Chi-Square
Least Squares
Bayes Method
Benefits of Bayesian Statistics
Comparison of Bayesian Statistics
Classical Statistical Prior Distributions
Posterior Distributions

Recommended Texts

Hogg, R. M. & Craig, A. T. (2019). Introduction to mathematical statistics. (7th ed.). New York: MacMillan Co.
Mood, A. M., Graybill, F. A. & Boes, D. C. (1997). Introduction to the theory of statistics. London: McGraw Hill.
Casella, G., & Berger, R. L. (2002). Statistical inference (Vol. 2, pp. 337-472). Pacific Grove, CA: Duxbury.
Hirai, A. S. (1973). Estimation of statistical parameters. Pakistan: IlmiKhana.
Lindgren, B.W. (1998). Statistical theory. New York: Chapman and Hall.
Stuart, A. & Ord, J. K. (1998). Kendall’s’ advanced theory of statistics (2nd ed.) London: Charles Griffin.

Week	Topics and Readings	Book name
1	Introduction to Statistical Inference	Statistical inference
2	Point of estimation, properties of good point estimators	Statistical Inference
3	Unbiasedness, Consistency, order distribution	Introduction to mathematical statistics
4	Sufficiency, Minimal sufficiency and joint sufficiency	Introduction to mathematical statistics
5	Exponential family	Introduction to mathematical statistics
6	Fisher information	Introduction to mathematical statistics
7	Cramer Rao Lower Bound	Introduction to mathematical statistics
8	Rao Blackwell and Lehmann Scheffe Theorem	Introduction to mathematical statistics
10	Methods of estimation	Introduction to mathematical statistics
11	Least squares and moments	Introduction to mathematical statistics
12	Bayes method	Introduction to mathematical statistics
13	Comparison of Bayesian and Classical methods	Introduction to mathematical statistics
14	Prior distribution and liklihood function	Statistical Inference
15	Posterior distributions generation	Statistical Inference
16	Benefits of Bayesian methods	Statistical Inference
17	Overview of previous	Statistical Inference