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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)