Homework 1
Jonathan Auerbach
February 13, 2015
Problem 1. Seven students volunteered for a comparison of study guides for an advanced course in
mathematics. They were randomly assigned, four to study guide A and three to study guide B. All were
instructed
Homework 2
Question 1.
(a) If we know to be 0, the unbiased estimator of the variance is
!
1
! =
(! )!
!
which is
!
!
! !
!
(
) =
!
!
!
!
The variables Zi are independent standard normal random variables, so ! /2 has a chi-square
distribution with n degre
Review of Basic Statistical
Procedures
Inference:
Estimation
Approaches:
Frequentist
Hypothesis
Testing
Bayesian
Type I error occurs when Ho is falsely rejected
Type II: When Ho is not rejected when it should be.
Note: [0,1]
Wilks Theorem: -2 ln () a
Advanced Data Analysis
Spring 2013
STAT W4201 ADVANCED DATA ANALYSIS
E-mail: alem@stat.columbia.edu
Office Hours: Friday: 5:00 PM - 6 PM,
and by appointment
TA: Chien-Hsu Huang: ch2526@columbia.edu
Prerequisites:
At least two of the following courses are
Generalized Linear Models II
Suppose there is a function g such that
Logistic Regression
Denote
Residuals
Interpretation of Coefficients
Overdispersion
Overdispersion (cont)
Special Cases
Implementation
R
R, glmnet package fitt:
glm(formula, family=poiss
Analysis of Variance
ANALYSIS OF VARIANCE
Examples: Data on blood pressure reductions
for patients receiving 3 different drugs.
Six patients randomized to each drug
Sitting diastolic pressure measured before
randomization (baseline) and after 4 weeks of
Linear Models (cont.)
OLS estimators, BLUE in the class of linear
unbiased estimators.
Model Validation
Linearity
Independence
Normality
Homoscedasticity
Influential Points
Robust Statistics
Multicollinearity
Ridge Regression
Principal Component
Survival Analysis
Survival Analysis
Properties of Survival Times
Note: The hazard function or the cumulative hazard function
NOT a probability. They are a measure of risk. The greater
the value of the cumulative hazard function, the greater the
risk of fa
Advanced Data Analysis
Fall 2015
IMPORTANT NOTICE!
Due to over-enrollment, class open ONLY
to Stat MA students who will graduate in
Dec 2015. NO EXCEPTION!
Stat MA and MAFN students must be in
their last semester to take the course.
The course will be off
Categorical Data Analysis
Test the relevant hypothesis.
> prop.test(13,100,0.15,alt="l")
1-sample prop test with continuity correction
X-square = 0.1765, df = 1, p-value = 0.3372
95 percent confidence interval:
0.0000000 0.2009056
Example. Suppose the man