The aim 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. Content includes: review of the key concepts of estimation, and construction of Normal-theory confidence intervals; frequentist theory of estimation including hypothesis tests;  methods of inference based on likelihood theory, including use of Fisher and observed information and likelihood ratio; Wald & score tests.

To produce the students, that has applicable knowledge about Inferential Statistics, which they apply in different fields. 

To impart applied knowledge about Inferential Statistics and its tools

To impart skills on the data collection, description measures of data interpretation of results, and decision making

After successfully completing the course, students will be able to:

Understand the philosophy and basic concepts of interval estimation and testing of hypothesis. Conduct appropriate interval and hypothesis tests for comparing population parameters. Demonstrate the ability to derive power functions and design of uniformly most powerful tests for continuous and discrete variables. Demonstrate understanding of the theory of maximum likelihood ration tests, sequential tests

Contents

Objective of statistical analysis and theory, criteria for the choice of families of models, the likelihood, sufficient statistics, some general principals of statistics inference, significance tests: simple null hypothesis and simple alternative hypothesis, some example, discrete problems, composite alternatives, two-sided tests, Local power, Multidimensional alternatives, composite null hypothesis, similar Region, invariants tests, Distribution– free and randomization tests: permutation tests, Rank test, Randomization tests, distance tests, Interval estimation: Scalar parameter, scalar parameter with nuisance parameters, Vector parameter, estimation of future observations, Point estimation: General considerations on bias and variance, Cramer–Rao inequality, Achievement of minimum variance and remove of bias, estimates of minimum mean squared error, Robust estimation, Asymptotic theory: Introduction, maximum likelihood estimates, large sample parametric significance tests, Robust inference for location parameters.

1. Hogg, R.V., Mckeen, J.W. And Craig, A.T. Introduction to Mathematical Statistics. 6th ed., Prentice Hall, New Jersey, (2005).
2. Hogg, R.,  Tanis E., and Zimmerman D., Probability and Statistical Inference. 9th ed., Prentice Hall, (2015).
3. Mood, A. M. Graybill, F. A. & Boes, D.C. Introduction to the Theory of Statistics, McGraw Hill, (1997).

Distribution of Marks:
Mid Exam:           30
Final exam:         50
Sessional (Assignment,Presentation,Participation,Attendance,Quizes)    20

Scheduled on:      Wednesday    (10:00-01:00)