Statistical Inference-I

Paper Code: 
STT 124
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course lays the foundation of Statistical Inference. The students would be taught the problems related to point and confidence interval estimation and testing of hypothesis. They would 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

STT-124

Statistical Inference-I

CO 16: Obtain the point estimator and interval estimator for the unknown population parameters.

 

CO 17: 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 18: Formulate hypothesis for a given problem.

 

CO 19: Apply the application of sequential statistical techniques on various probabilities.

 

CO 20: Perform a suitable non-parametric 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

 

15.00

Unit-I                                                                                                                

Point estimation, criteria of a good estimator: unbiasedness, consistency, efficiency and sufficiency. Concept of sufficient statistics, Fisher Neyman factorization theorem, Cramer-Rao inequality, Bhattacharya Bounds, Rao-Blackwell theorem, Completeness and Lehmann-Scheffe theorem, Uniformly minimum variance unbiased estimator, minimal sufficient statistic.

 

15.00

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.

 

15.00

Unit-III                                                                                                                

Statistical Hypothesis: Simple and composite, procedure of testing of hypothesis, critical region, types of errors, level of significance, p-value, power of a test, most powerful test and Neyman-Pearson fundamental lemma.

 

15.00

Unit-IV                                                                                                              

Sequential Analysis: Definition and construction of S.P.R.T. Fundamental relation among, A and B. Wald’s inequality for testing null hypothesis v/s alternative hypothesis. Determination of A and B Average sample number and operating characteristic curve, and determination of OC and ASN functions through Wald’s fundamental identity.

 

15.00

Unit-V                                                                                                          

Non-Parametric Tests: Sign tests, signed rank test, Kolmogorov-Smirnov one sample test. General two sample problems: Wolfowitz runs test, Kolmogorov Smirnov two sample test (for sample of equal size), Median test, Wilcoxon-Mann-Whitney U test. Test of randomness using run test based on the total number of runs and the length of a run. Kendall’s Tau test for independence of correlation, Kruskal Wallis K sample test and concept of asymptotic relative efficiency(ARE).

 

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. (1974): 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:

 

 

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: 
2022-2023
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