22BLUP(1)

# 22BLUP(1) - Prediction of random variables Key distinction...

This preview shows pages 1–3. Sign up to view the full content.

Prediction of random variables Key distinction between fixed and random effects: Estimate means of fixed effects Estimate variance of random effects But in some instances, want to predict FUTURE values of a random effect Example (from Efron and Morris, 1975, JASA 70:311-319): Baseball players. Given a player’s performance in the beginning of the season, predict performance in rest of season. c 2011 Dept. Statistics (Iowa State University) Stat 511 section 22 1 / 15 c 2011 Dept. Statistics (Iowa State University) Stat 511 section 22 2 / 15 c 2011 Dept. Statistics (Iowa State University) Stat 511 section 22 3 / 15 c 2011 Dept. Statistics (Iowa State University) Stat 511 section 22 4 / 15

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Best predictor is found by “Shrinking” obs. performance towards overall mean. So, how much shrinkage is needed? How do we compute optimal predictor? General answer using a linear mixed effects model y = X β + Zu + , where u N 0 0 , G 0 0 R Given data y , what is our best guess for values in the unobserved vector u ? c 2011 Dept. Statistics (Iowa State University) Stat 511 section 22 5 / 15 Because u is a random vector rather than a fixed parameter, we talk about predicting u rather than estimating u . We seek a Best Linear Unbiased Predictor (BLUP) for u , which we will denote by ˆ u To be a BLUP, we require 1. ˆ u is a linear function of y . 2. ˆ u is unbiased for u so that E ( ˆ u u ) = 0 . 3. Var ( ˆ u u ) is no “larger” than Var ( v u ) , where v is any other linear and unbiased predictor. It turns out that the BLUP for u is the BLUE of E ( u | y ) .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern