Lecture Notes

The lectures notes are available as single files mapped to the lecture sessions below or as a complete document ( PDF - 1.45MB).

LEC # TOPICS LECTURE NOTES
1

Estimation Theory

Introduction

( PDF)
2 Some Probability Distributions ( PDF)
3 Method of Moments ( PDF)
4 Maximum Likelihood Estimators ( PDF)
5

Consistency of MLE

Asymptotic Normality of MLE, Fisher Information

( PDF)
6 Rao-Crámer Inequality ( PDF)
7 Efficient Estimators ( PDF)
8

Gamma Distribution

Beta Distribution

( PDF)
9 Prior and Posterior Distributions ( PDF)
10

Bayes Estimators

Conjugate Prior Distributions

( PDF)
11 Sufficient Statistic ( PDF)
12

Jointly Sufficient Statistics

Improving Estimators Using Sufficient Statistics, Rao-Blackwell Theorem

( PDF)
13

Minimal Jointly Sufficient Statistics

χ2 Distribution

( PDF)
14 Estimates of Parameters of Normal Distribution ( PDF)
15 Orthogonal Transformation of Standard Normal Sample ( PDF)
16 Fisher and Student Distributions ( PDF)
17 Confidence Intervals for Parameters of Normal Distribution ( PDF)
18

Testing Hypotheses

Testing Simple Hypotheses

Bayes Decision Rules

( PDF)
19 Most Powerful Test for Two Simple Hypotheses ( PDF)
20

Randomized Most Powerful Test

Composite Hypotheses. Uniformly Most Powerful Test

( PDF)
21

Monotone Likelihood Ratio

One Sided Hypotheses

( PDF)
22 One Sided Hypotheses (cont.) ( PDF)
23 Pearson’s Theorem ( PDF)
24

Goodness-of-Fit Test

Goodness-of-Fit Test for Continuous Distribution

( PDF)
25 Goodness-of-Fit Test for Composite Hypotheses ( PDF)
26 Test of Independence ( PDF)
27 Test of Homogeneity ( PDF)
28 Kolmogorov-Smirnov Test ( PDF)
29

Simple Linear Regression

Method of Least Squares

Simple Linear Regression

( PDF)
30 Joint Distribution of the Estimates ( PDF)
31 Statistical Inference in Simple Linear Regression ( PDF)
32 Classification Problem ( PDF)

Course Info

Learning Resource Types

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assignment Problem Sets