B4090.HW7 - BTRY 4090 STSCI 4090 Spring 2011 Homework 7 Due...

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

View Full Document Right Arrow Icon
BTRY 4090 / STSCI 4090 Spring 2011 Homework 7 Due at 2:00pm on Friday, April 1 in 1198 Comstock Hall 1. We observe a random sample 1 2 , ,..., n X X X from the beta( θ ,1) distribution and an independent random sample 1 2 , ,..., m Y Y Y from the beta( λ ,1) distribution. (a) Find the generalized likelihood ratio test of H 0 : θ = λ versus H 1 : θ λ . Hint : Each step is routine: (1) Find the MLE of ( , )   over the parameter space {( , ) : 0, 0}     by writing the likelihood ( , ) L   and proceeding as usual. (2) Find the MLE of θ by writing the likelihood ( , ) L   , because {( , ) : , 0}   ; it is easier to recognize the resulting situation than to do the calculation, but either method works. (3) Compute the GLR. It looks pretty ugly initially – you wouldn’t want to bring it home to your mother – but this is OK, just write it down. We’ll see how well it cleans up in (b). (b) Define ln i i U X   for i = 1,2,…, n and ln j j V Y   for j = 1,2,…, m . Show that the
Image of page 1

Info icon This 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 ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern