Statistical Inference-II

Paper Code: 
STT 321
Credits: 
5
Contact Hours: 
75.00
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 undertake basic and applied research in Statistics.

 

Students will able to

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-321

Statistical Inference-I

CO 57: Know the notion of a parametric model and point estimation of the parameters of those models.

 

CO 58: Develop and construct most powerful statistical tests to test hypotheses regarding

unknown population parameters Using Neyman-Pearson Lemma and Likelihood Ratio

tests.

 

CO 59: Explain in detail elements of statistical decision problems and various inference problems viewed as decision problem.

 

CO 60: Explain in detail approaches to include a measure of accuracy for estimation procedures and our confidence in them by examining the area of interval estimation.

 

CO 61: Use Basic principle of Bayesian estimation for finding posterior distributions of unknown

Population parameters.

 

CO 62: Choose appropriate methods of inference to tackle real problems.

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

 

15.00

Unit-I                                                                                                                   

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

15.00

Unit –II                                                                                                      

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

15.00

Unit-III                                                                                                                  

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

 

15.00

Unit-IV                                                                                                                  

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.

 

15.00

Unit-V                                                                                                               

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.

 

References: 

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: 
2022-2023
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