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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).

LEC #TOPICSLECTURE NOTES
1Estimation Theory

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

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

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

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

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

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

Composite Hypotheses. Uniformly Most Powerful Test
(PDF)
21Monotone Likelihood Ratio

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

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

 








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