Lecture Notes

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

1 Estimation Theory

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

Beta Distribution
9 Prior and Posterior Distributions (PDF)
10 Bayes Estimators

Conjugate Prior Distributions
11 Sufficient Statistic (PDF)
12 Jointly Sufficient Statistics

Improving Estimators Using Sufficient Statistics, Rao-Blackwell Theorem
13 Minimal Jointly Sufficient Statistics

χ2 Distribution
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
19 Most Powerful Test for Two Simple Hypotheses (PDF)
20 Randomized Most Powerful Test

Composite Hypotheses. Uniformly Most Powerful Test
21 Monotone Likelihood Ratio

One Sided Hypotheses
22 One Sided Hypotheses (cont.) (PDF)
23 Pearson's Theorem (PDF)
24 Goodness-of-Fit Test

Goodness-of-Fit Test for Continuous Distribution
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
30 Joint Distribution of the Estimates (PDF)
31 Statistical Inference in Simple Linear Regression (PDF)
32 Classification Problem (PDF)