This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Outline Preliminaries Proof of E ( S 2 ) = 2 Proof of Var ( X + Y ) = Var ( X Y ) = 2 X + 2 Y for X , Y indep. Lab Assignment #4. Due date: 10/21. Email to Ms. Kraus. Lab4: Introduction to Statistical Simulations M. George Akritas M. George Akritas Lab4: Introduction to Statistical Simulations Outline Preliminaries Proof of E ( S 2 ) = 2 Proof of Var ( X + Y ) = Var ( X Y ) = 2 X + 2 Y for X , Y indep. Lab Assignment #4. Due date: 10/21. Email to Ms. Kraus. Preliminaries Proof by Simulation Matrices in R The apply function Proof of E ( S 2 ) = 2 Proof of Var( X + Y ) = Var( X Y ) = 2 X + 2 Y for X , Y indep. Lab Assignment #4. Due date: 10/21. Email to Ms. Kraus. M. George Akritas Lab4: Introduction to Statistical Simulations Outline Preliminaries Proof of E ( S 2 ) = 2 Proof of Var ( X + Y ) = Var ( X Y ) = 2 X + 2 Y for X , Y indep. Lab Assignment #4. Due date: 10/21. Email to Ms. Kraus. Proof by Simulation Matrices in R The apply function I A simulation consists of repeated generation of random samples and application of a statistical procedure on each sample. I It is used for providing numerical evidence in support of, or in contradiction to, certain probabilistic/statistical claims, or simply for investigating properties of a statistical procedure. I We will use simulations to verify that E ( S 2 ) = 2 , while E ( S ) 6 = . I In the process we will also verify that 1. As the sample size n ), S 2 2 , and S . 2. For independent X 1 , X 2 , Var( X 1 + X 2 ) = Var( X 1 X 2 ) = 2 1 + 2 2 M. George Akritas Lab4: Introduction to Statistical Simulations Outline Preliminaries Proof of E ( S 2 ) = 2 Proof of Var ( X + Y ) = Var ( X Y ) = 2 X + 2 Y for X , Y indep. Lab Assignment #4. Due date: 10/21. Email to Ms. Kraus. Proof by Simulation Matrices in R The apply function New terminology: Consistent and Unbiased estimators I Because S 2 2 , as n , we say that S 2 is a consistent estimator of 2 . S is also a consistent estimator of . I Because E ( S 2 ) = 2 , we say that S 2 is an unbiased estimator of 2 . I Because E ( S ) 6 = , S is a biased estimator of ....
View
Full
Document
This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Pennsylvania State University, University Park.
 Fall '00
 Akritas

Click to edit the document details