Statistics 550 Notes 18
Reading: Section 3.3-3.4
I. Finding Minimax Estimators (Section 3.3)
Review: Theorem 3.3.2 is a tool for finding minimax
estimators. It says that if an estimator is a Bayes est
Stat 550 Notes 19
Reading: Chapter 4.3
I. Uniformly Most Powerful Tests
When the alternative hypothesis is composite, H1 : 1 , then
the power can be different for different alternatives. For each
part
Statistics 550 Notes 18
Reading: Sections 4.1-4.2
I. Hypothesis Testing Motivation and Framework
Motivating Example: A graphologist claims to be able to
distinguish the writing of a schizophrenic pers
Statistics 550 Notes 17
Reading: Section 3.3
For finding minimax estimators, there is not a constructive
approach like for finding Bayes estimators and it is often
difficult to find the minimax estima
Statistics 550 Notes 16
Reading: Sections 3.2
I. Computation of Bayes procedures for complex
problems
For nonconjugate priors, the posterior mean (which is the
Bayes estimator under squared error loss
Statistics 550 Notes 15
Reading: Sections 3.1-3.2
In Chapter 3, we return to the theme of Section 1.3 which is
select among point estimators and decision procedures the
optimal estimator for the given
Statistics 550 Notes 14
Reading: Sections 2.4.3-2.4.4
I. Newtons Method
Newtons method is a numerical method for approximating
solutions to equations. The method produces a sequence of
values ( 0) , (
Statistics 550 Notes 13
Reading: Sections 2.4.2
The bisection method is a root finding algorithm which
works by repeatedly dividing an interval in half and then
selecting the subinterval in which the
Statistics 550 Notes 12
Reading: Section 2.3
I. Invariance Property of the MLE
Consider the model that the data X ~ p ( x | ), . For
an invertible mapping g ( ) , the model can be
reparameterized as X
Stat 550 Notes 20
Reading: Chapter 4.4-4.5, 4.7
I. Confidence Bounds, Intervals and Regions (Section 4.4)
A set estimate of is a set S ( X ) that is estimated to belong to
based on the sample X.
Examp
Statistics 550/Biostatistics 622: Mathematical Statistics
Fall 2009
Professor: Dylan Small
E-mail: [email protected]
Office: 464 Huntsman Hall
Class hours: Tuesday and Thursday, 10:30-11:50.
Of
Statistics 550 Notes 1
Reading: Section 1.1.
I. Basic definitions and examples of models (Section 1.1.1)
Goal of statistics: Draw useful information from data.
Model based approach to statistics: Trea
Statistics 550 Notes 11
Reading: Section 2.2.
Take-home midterm: I will e-mail it to you by Saturday,
October 14th. It will be due Wednesday, October 25th by 5
p.m.
I. Maximum Likelihood
The method of
Statistics 550 Notes 1
Reading: Section 1.1.
I. Basic definitions and examples of models (Section 1.1.1)
Goal of statistics: Draw useful information from data.
Model based approach to statistics: Trea
Take Home Midterm, Statistics 550, Fall 2006
This is a take home midterm exam and is due Wednesday, October 25th by 5 pm (put in
my mailbox in the statistics department or e-mail to me). You can consu
Homework 5, Statistics 550, Fall 2006
This homework is due Friday, October 13th by 5 p.m. You can put in my mailbox in the
statistics department on the fourth floor of Huntsman Hall if you do not hand
Statistics 550 Notes 15
Reading: Section 3.3
For finding minimax estimators, there is not a constructive
approach like for finding Bayes estimators and it is often
difficult to find the minimax estima
Statistics 550 Notes 14
Reading: Sections 3.2
I. Computation of Bayes procedures for complex
problems
For nonconjugate priors, the posterior mean (which is the
Bayes estimator under squared error loss
Stat 550 Notes 10
Reading: Chapter 3.4.2
We will give an outline of a proof of the asymptotic
optimality of the MLE:
Theorem: If n is the MLE and 0 is any other estimator,
then
%
ARE ( n , n ) 1 .
As
Stat 550 Notes 8
Notes:
1. We have no class this coming Tuesday because its fall
break.
2. The midterm is due at Wednesday by 5. Ill be around on
Monday and Tuesday if you have any questions about it.
Stat 550 Notes 11
Reading: Section 3.4.2
I. Asymptotic Relative Efficiency
Suppose that X 1 , K , X n ~ N ( ,1) . The MLE is n = X n , the
sample mean based on the n observations. Another reasonable
e
Stat 550 Notes 10
Reading Section 2.2
The likelihood function is defined by LX ( ) = p( X | ) .
The maximum likelihood estimator (the MLE), denoted by MLE
, is the value of that maximizes the likeliho
Stat 550 Notes 9
Reading: Section 2.2.
I. Maximum Likelihood
The method of maximum likelihood is a general approach to
point estimation.
Motivating Example: A purchaser of electrical components buys
t
Homework 9, Statistics 550, Fall 2009
This homework is due Friday, December 4th by 5 p.m. You can put in my mailbox in
the statistics department on the fourth floor of Huntsman Hall if you do not hand
Homework 9, Statistics 550, Fall 2009
This homework is due Friday, November 20th by 5 p.m. You can put in my mailbox in
the statistics department on the fourth floor of Huntsman Hall if you do not han
Homework 7, Statistics 550, Fall 2008
This homework is due Friday, November 13th by 5 p.m. You can put in my mailbox in
the statistics department on the fourth floor of Huntsman Hall if you do not han
Homework 6, Statistics 550, Fall 2009
This homework is due Friday, November 6th by 5 p.m. You can put in my mailbox in
the statistics department on the fourth floor of Huntsman Hall if you do not hand
Homework 5, Statistics 550, Fall 2009
This homework is due Friday, October 30th by 5 p.m. You can put in my mailbox in the
statistics department on the fourth floor of Huntsman Hall if you do not hand
Homework 4, Statistics 550, Fall 2009
This homework is due Friday, October 9th by 5 p.m. You can put in my mailbox in the
statistics department on the fourth floor of Huntsman Hall if you do not hand
Homework 3, Statistics 550, Fall 2009
This homework is due Friday, October 2nd by 5 p.m. You can put in my mailbox in the
statistics department on the fourth floor of Huntsman Hall if you do not hand