Calendar

The Problem sets are due one week after they are handed out.

LEC # TOPICS KEY DATES
1

Estimation Theory

Introduction

 
2 Some Probability Distributions Problem set 1 out
3 Method of Moments  
4 Maximum Likelihood Estimators Problem set 2 out
5

Consistency of MLE

Asymptotic Normality of MLE, Fisher Information

 
6 Rao-Crámer Inequality  
7 Efficient Estimators Problem set 3 out
8

Gamma Distribution

Beta Distribution

 
9 Prior and Posterior Distributions  
10

Bayes Estimators

Conjugate Prior Distributions

Problem set 4 out
11 Sufficient Statistic  
12

Jointly Sufficient Statistics

Improving Estimators Using Sufficient Statistics, Rao-Blackwell Theorem

 
13

Minimal Jointly Sufficient Statistics

χ2 Distribution

Problem set 5 out
14 Estimates of Parameters of Normal Distribution  
15 Orthogonal Transformation of Standard Normal Sample  
16 Fisher and Student Distributions  
17 Confidence Intervals for Parameters of Normal Distribution  
18

Testing Hypotheses

Testing Simple Hypotheses

Bayes Decision Rules

 
19 Most Powerful Test for Two Simple Hypotheses Problem set 6 out
20

Randomized Most Powerful Test

Composite Hypotheses, Uniformly Most Powerful Test

 
21

Monotone Likelihood Ratio

One Sided Hypotheses

 
22 One Sided Hypotheses (cont.) Problem set 7 out
23 Pearson’s Theorem  
24

Goodness-of-Fit Test

Goodness-of-Fit Test for Continuous Distribution

 
25 Goodness-of-Fit Test for Composite Hypotheses  
26 Test of Independence  
27 Test of Homogeneity Problem set 8 out
28 Kolmogorov-Smirnov Test  
29

Simple Linear Regression

Method of Least Squares

Simple Linear Regression

 
30 Joint Distribution of the Estimates  
31 Statistical Inference in Simple Linear Regression Problem set 9 out
32 Classification Problem  

Course Info

Learning Resource Types

notes Lecture Notes
assignment Problem Sets