Statistical Inference II

Paper Code: 
24DSTT801
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 hypotheses. They will also be given the concepts of nonparametric and sequential test procedures.

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24DSTT801

Statistical Inference II

(Theory)

 

CO 116: Identify and apply fundamental principles of statistical inference to effectively analyze and solve real-world statistical problems.

CO 117: Explain methods of estimation through practical applications in data analysis, ensuring accurate parameter estimation and inference.

CO 118: Apply the Neyman-Pearson fundamental lemma to various populations and utilize sequential statistical techniques to evaluate various probabilities.

CO 119: Evaluate large sample tests of significance and draw valid conclusions in practical situations.

CO 120: Demonstrate proficiency in applying advanced non parametric tests to analyze two-sample problems effectively.

CO 121: 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

 

12.00
Unit I: 
Statistical Inference Fundamentals

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: 
Method of estimation and Confidence intervals

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: 
Statistical Testing Fundamentals and Sequential Analysis

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 Tests and Non-Parametric Tests

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: 
Non-Parametric Tests

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

 

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:

 

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: 
2024-2025
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