Statistical Inference II

Paper Code: 
DSTT 801(A)
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This Paper aims at describing the concepts of Statistical Inference. The students would be taught the problems related to point and confidence interval estimation and testing of hypothesis. They will also be given the concepts of nonparametric and sequential test procedures.

 

Students will be able to:

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

DSTT 801(A)

Statistical Inference II

 

CO 103:  Learn the Cramer-Rao Inequality, Rao Blackwell and Lehmann Scheffe theorems and their applications in obtaining Minimum Variance Unbiased and Minimum Variance Bound estimators. 

 

CO 104: Obtain the point estimator and interval estimator for the unknown population parameters.

 

CO 105: Apply the concept of Neyman-Pearson fundamental lemma, in the context of hypothesis testing for Binomial, Poisson, Normal, and Exponential populations, for finding the best critical region.

 

CO 106: Apply the application of sequential statistical techniques on various probabilities.

 

CO 107: Perform a suitable non-parametric test and Large sample test for a given data.

Approach in teaching:

 

Interactive Lectures,

Group Discussion,

Classroom Assignment

Problem Solving Sessions

 

 

Learning activities for the students:

 

Assignments

Seminar

Presentation

Subject based  Activities

Classroom Quiz

Assignments

Class Test

Individual Presentation

 

 

12.00
Unit I: 

Fisher Neyman factorization theorem, Bhattacharya Bounds, Rao-Blackwell theorem, Completeness and Lehmann-Scheffe theorem, Uniformly minimum variance unbiased estimator, minimal sufficient statistic.

12.00
Unit II: 

Methods of Estimation: Maximum likelihood method, moments, minimum Chi-square and modified minimum Chi-square methods. Properties of maximum likelihood estimator (without proof). Confidence intervals: Determination of confidence intervals based on large samples, confidence intervals based on small samples.

12.00
Unit III: 

Basic idea of uniformly most powerful test & randomized and non-randomized test. Neyman-Pearson fundamental Lemma and its application for finding BCR. BCR in case of Binomial, Poisson and of Normal and Exponential Populations. Sequential Analysis: Definition and construction of S.P.R.T. Fundamental relation among, A and B.

12.00
Unit IV: 

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.

Non-Parametric Tests: Sign test, signed rank test, Run test, Kolmogorov-Smirnov one sample test.

12.00
Unit V: 

General two sample problems: Wolfowitz run test, Kolmogorov Smirnov two sample test (for sample of equal size), Median test, Wilcoxon-Mann-Whitney U test. Kendall’s Tau test for independence of correlation, Kruskal Wallis K sample test.

Essential Readings: 
  • Casela G & Berger RL. (2002): Statistical Inference. Duxbury Thompson Learning.
  • Conover WJ. (1980):  Practical Nonparametric Statistics. John Wiley.
  • Kiefer JC. (1987):  Introduction to Statistical Inference. Springer.
  • Lehmann EL. (1986) Theory of Point Estimation. John Wiley.
  • Wald A. (2004) Sequential Analysis. Dover Publ.
  • Cramer, H.(1946) : Mathematical methods of Statistics, Princeton University  Press
References: 

SUGGESTED READINGS:

● Goon and others.(2003): Outline of Statistical theory Vol-I, World Press.

●  Rao,C.R. (1973) : Linear Statistical inference and its applications, 2nd Ed, John Wiley & Sons Inc.

● Gibbons,J.D. (1985): Non- Parametric Statistical Inference, McGraw-Hill.

● Kendall, M.G. and Stuart, A. (1971): Advanced Theory of Statistic Vol. I and II,Charles Griffin.

● Mood, Graybill and Boes. (2007): Introduction to the theory of Statistics 3rded, McGraw- Hill.

● Hogg,R.V. and Craig,A.T.(2005): Introduction to Mathematical Statistics, Princeton University Press,sixth edition.

● Rao, C. R. (2002): Linear Statistical Inference and its Applications, Willey- Blackwell

● Gibbons (1971): Non Parametric Inference, Chapman and Hall

● Sidney and Siegal (1956):  Non Parametric for Behavioral science,Mcgraw-Hill Book Company

 

e-RESOURCES:

●  https://epgp.inflibnet.ac.in/

●  https://www.academia.edu/

●  https://www.slideshare.net/

● https://www.youtube.com/watchv=iin6vthyzsQ&list=PLbMVogVj5nJRkNUH5v9qNE...

 

JOURNALS: 

● Sankhya The Indian Journal of Statistics, Indian Statistical Institute

● Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University

● Afrika Statistika, Saint-Louis Senega University

● International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic

● Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics

● Journal of the Indian Statistical Association, Indian Statistical Association

● Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna Statistics and Applications, Society of Statistics, Computer and Applications

Academic Year: 
2023-2024
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