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Lecture Notes

Lecture Notes

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

1Estimation Theory

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

Asymptotic Normality of MLE, Fisher Information
6Rao-Crámer Inequality(PDF)
7Efficient Estimators(PDF)
8Gamma Distribution

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

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

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

χ2 Distribution
14Estimates of Parameters of Normal Distribution(PDF)
15Orthogonal Transformation of Standard Normal Sample(PDF)
16Fisher and Student Distributions(PDF)
17Confidence Intervals for Parameters of Normal Distribution(PDF)
18Testing Hypotheses

Testing Simple Hypotheses

Bayes Decision Rules
19Most Powerful Test for Two Simple Hypotheses(PDF)
20Randomized Most Powerful Test

Composite Hypotheses. Uniformly Most Powerful Test
21Monotone Likelihood Ratio

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

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

Method of Least Squares

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


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