Results 1 to 2 of 2

Math Help - Showing an estimate is an MLE

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    152

    Showing an estimate is an MLE

    Let X be Poisson. Consider a random sample of size n from the X distribution, and let Y be the sample sum.

    a) Show that Y/n is a maximum likelihood estimator of \lambda
    b) Show that the estimator in part (a) is unbiased and consistent.
    c) Also, show that Y/n is an efficient estimator of \lambda

    I'm just confused on what I have to show for each part of the question. I know they each have their requirements for what you have to show for each, I just don't remember and I don't have my book with me to check.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Quote Originally Posted by Janu42 View Post
    Let X be Poisson. Consider a random sample of size n from the X distribution, and let Y be the sample sum.

    a) Show that Y/n is a maximum likelihood estimator of \lambda
    b) Show that the estimator in part (a) is unbiased and consistent.
    c) Also, show that Y/n is an efficient estimator of \lambda

    I'm just confused on what I have to show for each part of the question. I know they each have their requirements for what you have to show for each, I just don't remember and I don't have my book with me to check.
    a) Your good on this one?

    b1) Unbiased means E(lambHat) = lamb. (Definitely true)

    b2) Consistent means lambHat -> lamb in probability. (True)

    c) Compare to fisher (asymptotic) variance. Use Cramer-Rao bound. (They will be equal in this case)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find a lower estimate and an upper estimate
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 17th 2010, 04:28 AM
  2. estimate
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 1st 2010, 09:18 PM
  3. Point estimate and Interval estimate
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 11th 2009, 09:42 AM
  4. Estimate mean and std dev?
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 9th 2009, 12:56 PM
  5. Big O Estimate
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 9th 2006, 11:23 PM

Search Tags


/mathhelpforum @mathhelpforum