Statistical Inference-I

Paper Code: 
24STT124
Credits: 
6
Contact Hours: 
90.00
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. 

 

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24STT124

Statistical Inference-I

(Theory)

CO 19: Demonstrate the criteria of a good estimator and demonstrate their application in statistical inference.

CO 20: Apply various methods of estimation effectively in practical statistical problems.

CO 21: Evaluate statistical hypotheses and apply hypothesis testing procedures on data.

CO 22: Explain the concept of sequential analysis and operating characteristic curves.

CO 23: Perform a suitable non-parametric test for a given data.

CO 24: 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: 
Estimation

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.

 

18.00
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.

 

18.00
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.

 

18.00
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.

 

18.00
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.

 

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

 

Academic Year: 
2024-2025
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