Statistical Inference-I

Paper Code: 
STT-124
Credits: 
3
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.

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper Title

 

 

 

 

 

STT124

 

 

 

 

Statistical Inference-I

(Theory)

 

 

 

 

 

 

The students will be able to –

 

CO15: Identify the samples following parametric and non-parametric distribution.

CO16: Obtain the point estimator and interval estimator of the parameters.

CO17: Apply the significance level as the probability of rejecting a true null hypothesis.

CO18: Construct and interpret a confidence interval about the population parameters.

CO19: Apply the application of sequential statistical techniques on various probabilities.

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Field trips

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

15.00

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

 

15.00

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

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

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

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: 

BOOKS RECOMMENDED

 

  • 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. (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

 

 

Academic Year: 
2020-2021
  • Printer-friendly version
  • PDF version