### 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.

• 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

Statistical Pre-requisities: 3(3-0)

Time Table:

MSC (3rd-Reg)

• Monday 9:00 AM - 10:00 AM
• Wednesday 10:00 AM -11:00 AM
• Thursday 11:00 AM - 12:00 AM

Distribution of Marks:
Mid Exam:           30

Final exam:          50
Sessional (Assignment,Presentation,Participation,Attendance,Quizes)    20