Course Archives Theoretical Statistics and Mathematics Unit
Course: Introduction to Statistical Inference
Level: Undergraduate
Time: Currently not offered
Syllabus
Past Exams


Syllabus:

For Prob III: All limit theorems used in this course will be stated in context with applications. These can be proved in Probability III rigorously.
i) Sufficiency, Exponential family, Bayesian methods, Moment methods, Maximum likelihood estimation.
ii) Criteria for estimators; UMVUE, Fisher Information.
iii) Multivariate normal distribution: Marginals, Conditionals; Distribution of linear forms.
iv) Order statistics and their distributions.
v) Large sample theory: Consistency, asymptotic normality, asymptotic relative efficiency.
vi) Elements of hypothesis testing; Neyman-Pearson Theory, UMP tests, Likelihood ratio and related tests, Large sample tests.
vii) Confidence intervals.

Reference Texts:

(a) George Casella and Roger L Berger: Statistical Inference.
(b) Peter J Bickel and Kjell A Doksum: Mathematical Statistics.
(c) Erich L Lehmann and George Casella: Theory of Point Estimation.
(d) Erich L Lehmann and Joseph P Romano: Testing Statistical Hypotheses.

Evaluation:
Midterm 35 marks
Assignments 15 marks
Final Exam 50 marks
Total 100 marks


Top of the page

Past Exams
Midterm
23.pdf

Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]