Statistical Inference

Paper Code: 
STT 401
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
Objective: 

This paper is designed to familiarize the students with concept of statistical inference which include estimation theory

10.00
Unit I: 
Large Sample Test of Significance

Testing of significance for attributes and variables, tests of significance for single mean, standard deviation and proportions, tests of significance for difference between two means, standard deviations and proportions.

8.00
Unit II: 
Theory of Estimation: Point Estimation

Problems of point estimation, properties of a good point estimator- unbiasedness, consistency, efficiency & sufficiency.-factorization theorem (without proof)and its applications.

9.00

Concept of mean square error, Minimum Variance Unbiased Estimation, Cramer Rao Inequality,  Rao-Blackwell Theorem (Without proof).Lehman Scheffe theorem(without proof), idea of most powerful test, uniformly most powerful test, randomised and non randomised test.

9.00
Unit IV: 
Methods of point estimation:

Method of Maximum Likelihood and its properties of MLEs (without proof). Methods of Moments: Least Squares method, interval estimation: Concept, confidence interval, confidence coefficient, construction of confidence interval for population mean, variance, difference of population mean when standard deviation are known and unknown of Normal Distribution.

9.00

Neyman pearson lemma and its application for finding BCR, BCR in case of binomial, poisson, normal,and exponential populations. non parametric tests: Definition, merits and limitations, Sign Test for univariate and bivariate distributions, run test and median testfor small and large samples.

Essential Readings: 

1. Goon, A.M., Gupta, M.K. and Dasgupta, B. Das (1991): An Outline of Statistics,
    Volume II, The World Press Pvt Ltd, Calcutta
2. Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, S Chand
    &Company, New Delhi.
3. Mood Alexander M., Graybill Frankline and Boes Duane C.: Introduction to Theory
    of Statistics, Mc Graw Hill & Company Third Edition
 

References: 

1. Rohatgi, V.K.(1967): An Introduction to Probability Theory and Statistics, John Wiley And Sons.
2. Casella,G. and Berger, Roger L.: Statistical Inference, Duxbury Thompson Learning ,Second Edition.
3. Snedecor, G.W. and Cochran, W.G. (1967): Statistical Methods, Iowa State University Press.
4. Gibbons, J. Dickinson and Chakraborthy, S.: Nonparametric Statistical Inference,
    CRC, Fourth Edition.
5. Rohatgi, V.K. and Saleh, A.K. Md. Ehsanes (2001): An Introduction to Probability
    Theory and Statistics, Second Edition, John Wiley andSons.
 

Academic Year: 
2019-2020
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