{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

h7 - Stat 5102(Geyer Spring 2012 Homework Assignment 7 Due...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Stat 5102 (Geyer) Spring 2012 Homework Assignment 7 Due Wednesday, March 21, 2012 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 7-1. Suppose X 1 , ... , X n are IID Cauchy( μ,σ ) and σ = 1 is known. We wish to do maximum likelihood estimation, which cannot be done in closed form, so you must use R. One needs a good estimate of the location param- eter to use as a starting point for the optimization. The location parameter is the center of symmetry and also the median. Thus the sample median is a good starting point. Data for the problem are at the URL http://www.stat.umn.edu/geyer/5102/data/prob7-1.txt (a) Find the MLE for these data. (b) Find the observed Fisher information evaluated at the MLE. (c) Find an asymptotic 95% confidence interval for the parameter μ . 7-2. Suppose x 1 , ... , x n are known numbers (not random), and we ob- serve random variables Y 1 , ... , Y n that are independent but not identically distributed random variables having distributions Y i ∼ N ( α + βx i 2 ) , where
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

h7 - Stat 5102(Geyer Spring 2012 Homework Assignment 7 Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online