Statistical Inference-II

Paper Code: 
25STT321
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course aims at describing the advanced level topics in statistical methods and statistical inference. This course would prepare students to have a strong base in basic statistics that would help them in undertaking basic and applied research in Statistics.

 

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

25STT321

Statistical Inference-II

(Theory)

CO 67: Identify the principles of location invariance and scale invariance in statistical estimation, and apply Pitman's estimators for location and scale parameters.

CO 68: Evaluate consistent asymptotic normal estimator and apply various tests based on Wilks likelihood ratio criteria.

CO 69: Explain the asymptotic distribution of likelihood ratio statistics and apply Bartlett's test for homogeneity of variances.

CO 70: Classify uniformly most powerful tests for two-sided hypothesis and apply generalized likelihood ratio tests for mean and variance.

CO 71: Explain in detail elements of statistical decision problems and various inference problems viewed as decision problems.

CO 72: Contribute effectively in course-specific interaction.

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

 

18.00
Unit I: 
Invariance Properties and Pitman's Estimators

Location Invariance, scale invariance. Pitmann’s estimators for location and scale parameters. Pitman concept of closeness of estimator. Proof of the properties of M.L.E(large samples), Huzur Bazaar theorem.

 

18.00
Unit II: 
Consistent Asymptotic Normal Estimators and Likelihood Ratio Tests

Consistent asymptotic normal (CAN) estimator, Invariance Property of CAN estimator. Wilks likelihood ratio criteria and the various test based on it.

 

18.00
Unit III: 
Asymptotic Distribution of Likelihood Ratio Statistic

Asymptotic distribution of likelihood ratio statistic. Bartlett's test for homogeneity of variances. Randomized tests. Generalized Neyman- Pearson lemma. 

 

 

18.00
Unit IV: 
Uniformly Most Powerful Tests and Generalized Likelihood Ratio Test

Uniformly most powerful tests for two-sided hypothesis. Unbiased tests. Uniformly most powerful unbiased tests, Generalized likelihood ratio test-mean and variance. Tests with Neyman’s Structures and its relation with complete family of distributions.

 

18.00
Unit V: 
Statistical Decision Problems and Decision Rules

Basic Elements of Statistical Decision Problem. Various inference problems viewed as decision problem. Randomization optimal decision rules. Bayes and minimax decision rule. ε-bayes & minimax decision rule, Generalized Bayes rule.

 

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.
  • 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. (2010): Non- Parametric Statistical Inference, McGraw-Hill, fifth edition.
  • Kendall, M.G. and Stuart, A. (1971): Advanced Theory of Statistic Vol. I and II,Charles Griffin.

 

SUGGESTED READINGS:

  • Mood, Graybill and Boes. (1974): Introduction to the theory of Statistics 3rded, McGraw- Hill.
  • Hogg,R.V. and Craig,A.T.( (1971): Introduction to Mathematical Statistics, Princeton University Press.
  • 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:

 

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
  • Stochastic Modeling and Applications, MUK Publications and Distributions

 

Academic Year: 
2025-2026
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