Stat 5102 (Geyer) Spring 2013
Homework Assignment 1
Due Wednesday, January 30, 2013
Solve each problem. Explain your reasoning. No credit for answers with
no explanation. If the problem is a proof, then you need words as well as
formulas. Explain why your
Stat 5102 (Geyer) Spring 2013
Homework Assignment 1 Solutions
1-1.
For the following data
2.2
1.4
0.8
3.2
2.0
1.0
3.6
1.8
3.6
1.6
1.8
0.4
2.2
0.2
1.0
2.0
1.2
2.2
2.4
2.4
(a) Find the mean of the empirical distribution.
(b) Find the variance of the empiric
Stat 5102 Final Exam
May 14, 2015
Name
Student ID
The exam is closed book and closed notes. You may use three 8 1 11
2
sheets of paper with formulas, etc. You may also use the handouts on brand
name distributions and Greek letters. You may use a calculato
SOLUTIONS FOR PROBLEM SET 1 STAT 5102-004 Given a parametric family of distributions, for parameter value and observable value y , let lik(|y ) = f (y |) be the likelihood at given y . Varying the parameter describes the likelihood function. (1) For any p
Stat 5102 (Geyer) Spring 2012 Homework Assignment 1 Due Wednesday, January 25, 2012
Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your
Stat 5102 (Geyer) Spring 2013
Homework Assignment 2
Due Wednesday, February 6, 2013
Solve each problem. Explain your reasoning. No credit for answers with
no explanation. If the problem is a proof, then you need words as well as
formulas. Explain why your
SOLUTIONS TO PROBLEM SET 2 STAT 5102-004 (1) Suppose we are interested in the proportion of defective items in a large population. Consider taking a sample from that population. If the population is large compared to any sample we might see, we can safely
Stat 5102 (Geyer) Spring 2010 Homework Assignment 2 Due Wednesday, February 3, 2010
Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your
Stat 5102 (Geyer) Spring 2013
Homework Assignment 2 Solutions
2-1. Suppose X1 , X2 , . . . are IID Unif(0, ). As usual X(n) denotes the
n-th order statistic, which is the maximum of the Xi .
(a) Show that
P
X(n) ,
as n .
(b) Show that
D
n X(n) Exp(1/),
as
Stat 5102 First Midterm Exam
October 12, 2016
Name
Student ID
The exam is closed book and closed notes. You may use one 8 12 11 sheet
of paper with formulas, etc. You may also use the handouts on brand name
distributions and Greek letters. You may use a c
Stat 5102 Notes: Markov Chain Monte Carlo and
Bayesian Inference
Charles J. Geyer
March 30, 2012
1
The Problem
This is an example of an application of Bayes rule that requires some
form of computer analysis. We will use Markov chain Monte Carlo (MCMC).
Th
Stat 5102 (Geyer) Spring 2013
Homework Assignment 8 Solutions
8-1. Show that each of the following is an exponential family. Identify the
natural parameter and natural statistic.
(a) The Poi() family of distributions.
(b) The Exp() family of distributions
Stat 5102 (Geyer) Spring 2013
Homework Assignment 6 Solutions
6-1. Suppose X1 , X2 , . . ., Xn are IID Exp(). Find the likelihood function
and log likelihood function.
Solution. The PDF for one observation is
f (x) = ex
The joint PDF for n observations is
Stat 5102 (Geyer) Spring 2013
Homework Assignment 5 Solutions
5-1. In each of the situations below explain whether a one-tailed or a twotailed test is more appropriate. If you cant tell, give arguments for both
sides.
(a) Two groups are considered indepen
Stat 5102 (Geyer) Spring 2013
Homework Assignment 4 Solutions
4-1. Calculate the ARE of the sample mean X n versus the sample median
Xn as an estimator of the center of symmetry for
(a) The Laplace location-scale family having density given in the brand
n
Stat 5102 (Geyer) Spring 2013
Homework Assignment 3 Solutions
3-1. Show that the family of Gam(, ) distributions with known and
unknown, so the parameter space is
cfw_ R : > 0
is a scale family.
Solution. The problem is to show that if Y Gam( , ), where
Stat 5102 Lecture Slides: Deck 7
Model Selection
Charles J. Geyer
School of Statistics
University of Minnesota
1
Model Selection
When we have two nested models, we know how to compare
them: the likelihood ratio test.
When we have a short sequence of neste
Stat 5102 (Geyer) Spring 2013
Homework Assignment 7 Solutions
7-1. Suppose X1 , . . ., Xn are IID Cauchy(, ) and = 1 is known. We
wish to do maximum likelihood estimation, which cannot be done in closed
form, so you must use R. One needs a good estimate o
Stat 5102 Lecture Slides
Deck 3
Charles J. Geyer
School of Statistics
University of Minnesota
1
Likelihood Inference
We have learned one very general method of estimation: the
method of moments.
Now we learn another: the method of maximum likelihood.
2
Li
Stat 5102 Lecture Slides
Deck 8
Charles J. Geyer
School of Statistics
University of Minnesota
1
Plug-In and the Bootstrap
The worst mistake one can make in statistics is to confuse the
sample and the population or to confuse estimators and param
eters. In