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

1 Estimation Theory

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