ST202 P ROBABILITY, D ISTRIBUTION T HEORY, AND I NFERENCE
Erik Baurdoux
Michaelmas Term 2013-2014
This version December 10, 2013
33
Bernoulli motivation
This section starts off somewhat more abstract but concludes with the most important and
widely-used t
Hypothesis Testing Schematic
1. State the null and alternative
2. State the models: unrestricted and restricted
3. State the test statistic and its distribution under the null
4. Find the acceptance / rejection region
5. Specify the significance level
6.
EC221 Lecture Notes: Michaelmas
Term
Contents
We start with a quick review of the required mathematical content (10 pages), and then
recall all basic statistical knowledge, that is assumed for this course (26 pages).
We then start with the content for the
EC221 Tips and Comments
1. READ QUESTION
2. 1.96 5% two sided test, 1.64 5% one sided test
3. In talking about diference between one and two sided test, ALWAYS mention power.
4. WRITE NEATLY AND USE EQUATION NUMBERS
5. ASSUMPTIONS IN TESTS
6. HYPOTHESIS T
EC221 Regression Doctor
How to run a regression
First step: test all slopes
Second step: test the significance of the regression
Check the correlation between regressors
Run the residuals on and check that is approximately - and slopes should all fail to
EC221 Derivations and Proofs
A Linear Algebra Review
B Statistical Review
1 Classical Simple Linear Regression Model
1.1 Introduction
1.2 Classical (Gauss-Markov) Linear Regression
Assumptions
Variance of result:
Given assumptions , show that .
Recall , h
Proof
We show that:
Or
Recall:
Thus:
First, realise that:
And that:
Hence:
Second, realise that:
Recall from the Central Limit Theorem that for random variable :
Taking , since , we have:
We have via the law of iterated expectations that:
Putting it all t
3 Hypothesis Testing
We split this chapter up into six distinct sections. Learn each of the sections, and each of the
subsections in each section.
3.0 Introduction
In the previous chapter we developed the following two exact sampling distributions of and
Summer 2011 Examination
EC221
Principles of Econometrics
2010/2011 syllabus only not for resit candidates
Instructions to candidates
Time allowed: 3 hours + 15 minutes reading time
The rst 15 minutes is a reading period. During the reading period you
cann
Notes
EC221: Principles of Econometrics
Specication Issues
Dr M. Schafgans
London School of Economics
Michaelmas 2013
(London School of Economics)
EC221: Specication
Michaelmas 2013
1 / 17
Notes
Selecting the Set of Regressors
(London School of Economics)
Notes
EC221: Principles of Econometrics
Asymptotic Theory
MLE: Trinity of Classical Testing
Dr M. Schafgans
London School of Economics
Michaelmas 2013
(London School of Economics)
EC221: Asymptotics & MLE
Michaelmas 2013
1 / 57
Notes
Large (asymptotic) Sa
Key Business Cycle Facts: Summary
Variable
Cyclicality
Consumption
Investment
Price Level
Money Supply
Lead
Coincident
Lag
Procyclical
Coincident
Proccal
oincident
Countercyclic
Coincident
al
Procyclical
Leading
Variation Relative to Notes and Tips
GDP
L
EC210 Growth Models
Short Summary
This is a short summary of the growth models we studied in the course.
It summarises the key equations for each model. It is not a substitute for lecture notes.
The term state variable refers to a variable that describes
EC210 Q&A
Handout 1
1. Why is now the most interesting time to study Macroeconomics?
2. Give an example of a macroeconomic event in the past 2 years.
3. What is our main method of study in EC210?
4. What is the main topic of study in EC210?
5. What is our
The Solow Model A Note
We aim to derive the steady state of the Solow Model.
We start by stating the assumed production function for the economy:
Where are respectively the output, technology, capital, labour, and production function for
the given economy
Classical (Gauss-Markov) Linear Regression
Assumptions
If we believe that any of these are not likely to hold, we must really consider whether or not we should be using the model
(A.1)
True model is
We assume a linear relationship between and . is a measu
EC221 Proofs I Know
1. Derivation of Wald Test
2.
- not in course pack but you got it!
3.
unbiased
4.
equals probability of Type error
5.
such that
6.
implies , for
7. The Gauss Markov Theorem
8.
unbiased
9. Distribution of
10.
11.
12. Derivation of
13. c
ST202 Probability Distribution Theory and Inference
Lecture Notes - Part I
Lecturer: Kostas Kalogeropoulos (Oce B610)
Lent Term 2014
1
Properties of a Random Sample
Reading
G. Casella & R. L. Berger 2.1 4.3 4.6 5.1 5.2 5.3 5.4
1.1
Samples and Statistics
A
ST202 Probability Distribution Theory and Inference
Lecture Notes - Part II
Lecturer: Kostas Kalogeropoulos (Oce B610)
Lent Term 2014
1
Point Estimation
Reading
G. Casella & R. L. Berger 7.1 7.2.1 7.2.2 7.3.1 7.3.2 7.3.3
Problem:
Suppose that a real worl
ST202: Lent Term - Statistical Inference
Week 7: Asymptotic Evaluations on Estimation
Kostas Kalogeropoulos
Week 7 LT 2014
Kostas Kalogeropoulos
ST202 Week 7: Asymptotic Estimation
Summary - Point Estimation
In point estimation we use the information from
ST202: Lent Term - Statistical Inference
Week 6: Interval Estimation
Kostas Kalogeropoulos
Week 6 LT 2014
Kostas Kalogeropoulos
ST202 Week 6: Interval Estimation
Interval Estimators and Condence Sets
Point estimates provide a single value as a best guess
ST202: Lent Term - Statistical Inference
Week 8: Hypothesis Testing I
Kostas Kalogeropoulos
Week 8 - LT 2012
Kostas Kalogeropoulos
ST202 Week 8: Hypothesis Testing I
Hypothesis Testing Problem
Suppose that a real world phenomenon / population may be
descr
Useful Results
Matteo Barigozzi
Series and Expansions
1. Taylor series: for a function f with continuous derivatives, j th derivative
denoted f (j) ;
f (x) = f (a) + f (a)(x a) +
1
1
f (a)(x a)2 + . . . + f (j) (a)(x a)j + . . .
2!
j!
2. MacLaurin Series:
ST202: Lent Term - Statistical Inference
Week 10: Hypothesis Testing III
Kostas Kalogeropoulos
Week 10 - LT 2014
Kostas Kalogeropoulos
ST202 Week 10: Hypothesis Testing III
Likelihood ratio test
Let = 0 c and consider hypothesis testing problems with
0
H0
EC202 Microeconomic Principles II: Lecture 2
Leonardo Felli
CLM.G.02
23 January 2014
First-Price Auction
Two bidders N = cfw_1, 2;
Both bidders can submit any non-negative bid:
A1 = cfw_b1 0
A2 = cfw_b2 0
We assume that the value of the good to each bidde