Statistical Inference for FE. Mathematical Formula Sheet. 2 /n1 F -distribution Fn1 ,n2 = n1 /n2 , where 2 1 and 2 2 are two independent 2 distribution with d.f. n1 2 n n and n2 , respectively. Fn1 , = 2 1 /n1 , where 2 1 is a 2 distribution with d.f. n1
Statistical Inference for FE Professor S. Kou, Department of IEOR, Columbia University Lecture 1. Basic Estimation Principles
1
Introduction to Statistics
What is Statistics? Statistics is the study of collecting, analyzing, and interpreting quantitative
E4702. Statistical Inference for FE. Professor S. Kou. Sample Midterm Solution, Summer 2009, 8/12/2007, 11amm-1:30pm. Closed Book Exam. Total 40 pts. 1. (5 pts) (a) (1 pt) St. Petersburg Stock Exchange in Russia. (b) (2 pts) A natural estimator for 1 - 2
E4708. Statistical Inference for FE. Professor S. Kou. Final Exam, Aug 26, 2009. Closed Book Exam. Total 50 pts. Note: For "true or false"questions, simply answer "true"or "false" No explanation is needed. . 1. (7 pts) Basic Facts from Empirical Finance.
Statistical Inference for FE Professor S. Kou, Department of IEOR, Columbia University Lecture 2. Properties of MLE and Estimation for Geometric Brownian Motion
1
Properties of MLE's
MLE is perhaps the most widely used estimation procedure, mainly because
IEOR E4702 Statistical Inference for Financial Engineering
HWK Solution 2
1. The likelihood L is given by L= Therefore, log L = = Now @ log L = @ Thus, the MLE is given by n+
n X i=1 n Y i=1
f (Xi j ) =
n Y i=1
e
( )Xi Xi !
(
+ Xi log
n X i=1
log(Xi !)
n
Statistical Inference for FE Professor S. Kou, Department of IEOR, Columbia University Lecture 3. Hypothesis Testing
1
1.1
Introduction to Hypothesis Testing
Confidence Intervals and Hypothesis Testing
How to test the hypothesis H0 : = 3 versus the altern
Columbia University Department of IEOR Statistical Inference for Financial Engineering E4702, Summer 2010 TR 3pm-5:30pm, 633 Mudd Columbia Course Work Web Page Prof. Steven Kou 312 Mudd Building [email protected] Tel: 212-854-4334 Professor's Office Hours
E4702. Statistical Inference for Financial Engineering. Professor S. Kou. Midterm, August 12, 2010. 11am-1:30pm. Closed Book Exam. Total 40 pts. Note: For "true or false"questions, simply answer "true"or "false" No explanation is needed. . 1. (5 pts) The
Poisson distribution
BAYESIAN ANALYSIS: Week 3 and 4 - Poisson Distribution
July 3rd and 17th 2008
This week we are interested in the Poisson distribution. We first look at the probability density function and discuss some of its properties. We then compu
Connexions module: m13500
1
Maximum Likelihood Estimation Examples
Ewa Paszek
This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License
Abstract
This course is a short series of lectures on Introductory St
E4702. Statistical Inference for Financial Engineering. Professor S. Kou. Midterm, August 12, 2009. 11am-1:30pm. Closed Book Exam. Total 40 pts. Note: For "true or false"questions, simply answer "true"or "false" No explanation is needed. . 1. (5 pts) Basi
Statistical Inference for FE Professor S. Kou, Department of IEOR, Columbia University Lecture 6. Introduction to Statistical Computing
1
Newton-Raphson's Method to Compute the MLE
One way to compute the MLE is the classical Newton-Raphson's method, as we
Statistical Inference for FE Professor S. Kou, Department of IEOR, Columbia University Lecture 5. Bayesian Inference
1
Introduction
So far we have focused on point estimation and hypothesis testing via frequentist methods. The frequentist method is based
Statistical Inference for FE Professor S. Kou, Department of IEOR, Columbia University Lecture 4. Goodness-of-Fit Tests In this lecture we shall study various goodness-of-fit tests, whose objective is to test whether a model fits data. We shall introduce
IEOR E4702 Statistical Inference for Financial Engineering
HWK Solution 5
1. (a) The likelihood for X1 , ., Xn is given by f (X|) = The prior density is -1 e-/ . () Therefore, the posterior is given by f (|X)
n -1 e-/ Y - Xi e () Xi ! i=1 n Y n Y i=1
e-
IEOR E4702 Statistical Inference for Financial Engineering
HWK Solution 4
1. a. Denote Xi 's the samples, i = 1, . . . , n, and Oi 's frequencies Oi , i = 1, . . . , 12. With the assumption of geometric distribution and statistical independence of samples
IEOR E4702 Statistical Inference for Financial Engineering
HWK Solution 3
1. Under H0 the likelihood is given by LH0 (0 ) = and log LH0 (0 ) = -n0 + log(0 ) Without constraints under Ha , we have log LHa () = -n + log()
Pn
n Y
i=1
f (Xi |0 ) =
i=1
n Y
e-0
E4702. Statistical Inference for FE. Professor S. Kou. Final Exam, August 26, 2009, 11am-1:30pm. Closed Book Exam. Total 50 pts. Note: For "true or false" questions, simply answer "true" or "false" No explanation is needed. . 1. (7 pts) Basic Facts. (a) (
Default Clustering and Pricing of CDO' s
Xian Hua Peng and Steven Kou Columbia University
Xian Hua Peng and Steven Kou Columbia University ()
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1
The Recent Financial Turmoil
2
What is a CDO?
3
Current Portfolio Credit Risk Models
4
The New Condition