Courses » Statistical Inference

Statistical Inference


Sir R.A. Fisher published two seminal papers on the foundations of statistical inference in 1922 and 1925. These and subsequent publication of his book “Statistical Methods for Research Workers” led to a revolutionary use of statistical ideas in all branches of science, engineering, medical, biology and social sciences. Shortly afterwards the testing of hypothesis was given a firm theoretical foundation by J. Neyman and E.S. person in a series of papers. In the last ninety years the two topics of estimation and testing of hypothesis have become inseparable part of any scientific investigation. As the scientists in various areas need to use these methods, the students need to learn the basics of the theory behind these. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage. Each concept has been explained through examples and problems.

Students studying Major in Statistics, Mathematics, all engineering disciplines aspiring for a career in data science and data analytics. The students of Computer Science and Engg, Electronics and Communications, Electrical, Industrial, Mechanical, Chemical, Economics, Biotechnology, Mining, Agriculture and Food Technology etc. can take this course



PREREQUISITES: Students must have done a basic course in Probability, Distributions and Statistics. They must have good knowledge of differential and integral calculus, sequences and series, basic linear/matrix Algebra (usually students who have completed Mathematics-I and II at first year undergraduate level)

INDUSTRY SUPPORT: All companies which deal with data/business analytics will recognize this course. Today all industries use statistical methods. So for students desirous to work in any type of industry, this course will be indispensable. In particular, companies dealing with Business Analytics, Banking and finance, Insurance, machine learning, data mining etc. this course will be invaluable.

1220 students have enrolled already!!


Prof. Somesh Kumar is a professor in the Department of Mathematics, IIT Kharagpur. He has over 30 years of experience of teaching courses on Probability Statistics, Statistical Inference, Sampling Theory, Stochastic Processes, Multivariate Analysis, Regression analysis, Time Series, Experimental Designs, Decision Theory to undergraduate, postgraduate and doctorate students. His NPTEL courses (under MHRD) on Probability and Statistics, Statistical Inference and Statistical Methods for Scientists and Engineers (each of 40 hours) are available online and very popular. He has also taught Mathematics-I in QEEE program of MHRD to 130 engineering college students in online mode during Autumn 2014-2015. He offered the course “Probability and Statistics” for certification program in Jan-April 2016 and in Jan-April 2017. His lectures on “Probability” and “Permutation and combinations” for class XII students under IIT-PAL scheme of MHRD are also available through DTH channels of national television.His research interests are Statistical Decision Theory, Estimation Theory, Testing of Hypothesis, Classification Problems, Directional Distributions, Limit Theorems. He has published more than 80 research papers in refereed reputed international journals and book chapters. He has supervised ten Ph.D. students and more than two hundred Masters (M.Tech./ M.Sc./B.Tech.) dissertations.He has been guest professor in University of Ulm, Germany in July 2017 and June-July 2018. He is Principal Investigator for a major research project “Drone for Vaccine Delivery” funded by the Indian Council for Medical Research. He has delivered invited lectures in various universities in India and abroad.


Week 1  :

1. Introduction and Motivation – I

2. Introduction and Motivation – II

3. Basic Concepts of Point Estimations – III

4. Basic Concepts of Point Estimations – IV

5. Basic Concepts of Point Estimations – V

Week 2  :  

6 .Basic Concepts of Point Estimations – VI
7. Finding Estimators – I
8. Finding Estimators – II
9. Finding Estimators – III
10.Finding Estimators – IV

Week 3 

11.Finding Estimators – V

12.Finding Estimators – VI

13.Properties of MLEs – I

14.Properties of MLEs – II

15.Lower Bounds for Variance – I

Week 4  :  

16.Lower Bounds for Variance – II

17.Lower Bounds of Variance – III

18.Lower Bounds of Variance – IV

19.Lower Bounds of Variance – V

20.Lower Bounds of Variance – VI

Week 5  :  

21.Lower Bounds of Variance – VII

22.Lower Bounds of Variance – VIII

23.Sufficiency – I 

24.Sufficiency – II

25.Sufficiency and Information – I 

Week 6  :  

26.Sufficiency and Information – II

27.Minimal Sufficiency, Completeness – I

28.Minimal Sufficiency, Completeness – II

29.UMVU Estimation, Ancillarity – I

30.UMVU Estimation, Ancillarity – II 

Week 7  :  

31.Testing of Hypotheses: Basic Concepts – I

32.Testing of Hypotheses: Basic Concepts - II

33.Neyman Pearson Fundamental Lemma – I

34.Neyman Pearson Fundamental Lemma – II

35.Application of NP Lemma – I 

Week 8  :  

36. Application of NP Lemma – II UMP Unbiased Tests – II

37. UMP Tests – I

38.UMP Tests – II

39.UMP Tests – III

40.UMP Tests – IV

Week 9  :  

41.UMP Unbiased Tests – I
42.UMP Unbiased Tests – II

43.UMP Unbiased Tests – III

44.UMP Unbiased Tests – IV

45.Applications of UMP Unbiased Tests – I

46.Applications of UMP Unbiased Tests – II

Week 10 

47.Unbiased Tests for Normal Populations – I

48.Unbiased Tests for Normal Populations – II

49.Unbiased Tests for Normal Populations – III

50.Unbiased Tests for Normal Populations - IV

51.Likelihood Ratio Tests – I

52.Likelihood Ratio Tests – II

Week 11 

53.Likelihood Ratio Tests – III

54.Likelihood Ratio Tests – IV

55.Likelihood Ratio Tests – V

56.Likelihood Ratio Tests – VI

57.Likelihood Ratio Tests – VII

58.Likelihood Ratio Tests – VIII

Week 12 

59.Test for Goodness of Fit – I

60.Test for Goodness of Fit – II

61.Interval estimation – I

62.Interval estimation – II 

63.Interval estimation – III

64.Interval estimation – IV


1. An Introduction to Probability and Statistics by V.K. Rohatgi & A.K. Md. E. Saleh.
2. Statistical Inference by G. Casella & R.L. Berger.
3. A First Course on Parametric Inference by B.K. Kale
4. Modern Mathematical Statistics by E.J. Dudewicz & S.N. Mishra5. Introduction to the Theory of Statistics by A.M. Mood, F.A. Graybill and D.C. Boes  
  • The exam is optional for a fee.
  • Date and Time of Exams: April 27 (Saturday)  Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
  • Registration url: Announcements will be made when the registration form is open for registrations.
  • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.


  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 8 out of 12 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur.It will be e-verifiable at nptel.ac.in/noc.