Stat 5132 (Geyer) Old First Midterm

Stat 5132 (Geyer) Old First Midterm - it Problem 4 Suppose...

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

View Full Document Right Arrow Icon
Up: Stat 5132 Stat 5132 First Midterm Exam, February 4, 1998 Problem 1 Let be the sample median for an i. i. d. sample of size n from the model having densities where is an unknown parameter, .Find the asymptotic distribution of . Problem 2 Let X 1 , X 2 , , X n be an i. i. d. sample from a model, and let S 2 n be the sample variance Calculate the probability in the case n = 10. Problem 3 Let X 1 , X 2 , , X n be an i. i. d. sample from a model having densities where is an unknown parameter. Find the MLE of . You do not have to prove that your solution is the global maximizer of the likelihood. It is enough to find
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
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: it. Problem 4 Suppose U and V are statistics that are both unbiased estimators of a parameter . Write and ,and define another statistic T = a U + (1 - a ) V where a is an arbitrary but known constant. a. Show that T is an unbiased estimator of . b. Find the a that gives T the smallest mean square error. Problem 5 Calculate the (expected) Fisher information for a model, where is an unknown parameter (i. e. ). Up: Stat 5132 Charles Geyer 1/2/1999...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Stat 5132 (Geyer) Old First Midterm - it Problem 4 Suppose...

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

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