×
Log in to StudySoup
Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 9 - Problem 66e
Join StudySoup for FREE
Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 9 - Problem 66e

Already have an account? Login here
×
Reset your password

The likelihood function L(y1, y2, . . . , yn | ?) takes on

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 66E Chapter 9

Mathematical Statistics with Applications | 7th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

4 5 1 354 Reviews
18
4
Problem 66E

Problem 66E

The likelihood function L(y1, y2, . . . , yn | θ) takes on different values depending on the arguments (y1, y2 , . . . , yn ). A method for deriving a minimal sufficient statistic developed by Lehmann and Scheff´e uses the ratio of the likelihoods evaluated at two points, (x1, x2, . . . , xn) and (y1, y2, . . . , yn ):

Many times it is possible to find a function g(x1, x2, . . . , xn ) such that this ratio is free of the unknown parameter θ if and only if g(x1, x2, . . . , xn ) = g(y1, y2, . . . , yn ). If such a function g can be found, then g(Y1, Y2, . . . , Yn ) is a minimal sufficient statistic for θ .

a Let Y1, Y2, . . . , Yn be a random sample from a Bernoulli distribution (see Example 9.6 and Exercise 9.65) with p unknown.

i Show that

ii Argue that for this ratio to be independent of p, we must have

iii Using the method of Lehmann and Scheff´e, what is a minimal sufficient statistic for p? How does this sufficient statistic compare to the sufficient statistic derived in Example 9.6 by using the factorization criterion?

b Consider the Weibull density discussed in Example 9.7.

i Show that

Reference

In this exercise, we illustrate the direct use of the Rao–Blackwell theorem. Let Y1, Y2, . . . , Ynbe independent Bernoulli random variables with

Step-by-Step Solution:
Step 1 of 3

Chapter 4: General Features of Cells Overview ­ Cell biology: the study of individual cells and their interactions with each other ­ Cell theory: o All living organisms are composed of one or more cells o Cells are the smallest units of life o New cells come only from pre­existing cells by division 4.1 Microscopy ­ Overview o Microscope: a magnification tool that enables researchers to study the structure and function of cells  Compound microscope: a microscope with more than one lens o Micrograph: an image taken with the aid of a microscope o Resolution: a measure of the clarity of an image  Ability to observe two objects as d

Step 2 of 3

Chapter 9, Problem 66E is Solved
Step 3 of 3

Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This full solution covers the following key subjects: sufficient, Statistic, function, Example, ratio. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The full step-by-step solution to problem: 66E from chapter: 9 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Since the solution to 66E from 9 chapter was answered, more than 282 students have viewed the full step-by-step answer. The answer to “The likelihood function L(y1, y2, . . . , yn | ?) takes on different values depending on the arguments (y1, y2 , . . . , yn ). A method for deriving a minimal sufficient statistic developed by Lehmann and Scheff´e uses the ratio of the likelihoods evaluated at two points, (x1, x2, . . . , xn) and (y1, y2, . . . , yn ): Many times it is possible to find a function g(x1, x2, . . . , xn ) such that this ratio is free of the unknown parameter ? if and only if g(x1, x2, . . . , xn ) = g(y1, y2, . . . , yn ). If such a function g can be found, then g(Y1, Y2, . . . , Yn ) is a minimal sufficient statistic for ? .a Let Y1, Y2, . . . , Yn be a random sample from a Bernoulli distribution (see Example 9.6 and Exercise 9.65) with p unknown.i Show that ii Argue that for this ratio to be independent of p, we must have iii Using the method of Lehmann and Scheff´e, what is a minimal sufficient statistic for p? How does this sufficient statistic compare to the sufficient statistic derived in Example 9.6 by using the factorization criterion?b Consider the Weibull density discussed in Example 9.7.i Show that ReferenceIn this exercise, we illustrate the direct use of the Rao–Blackwell theorem. Let Y1, Y2, . . . , Ynbe independent Bernoulli random variables with” is broken down into a number of easy to follow steps, and 253 words.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

The likelihood function L(y1, y2, . . . , yn | ?) takes on