Results 1 to 5 of 5

Math Help - Maximum likelihood estimation

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    The UK
    Posts
    5

    Question Maximum likelihood estimation

    I really appreciate if somebody can help me to answer this question;

    A sample of size n is drawn from each of two normal populations, both of which have variance ��2. The mean of the two populations are (a+b) and (a-b), respectively, where a,b>0. The sample observations are denoted xij, i=1,2 and j=1,...,n. The question is " What are the maximum likelihood estimators of a,b, ��2?

    Thanks in advance.



















    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,879
    Thanks
    697

    Re: Maximum likelihood estimation

    He Bewar.

    What are the normal MLE's for the means of a distribution? Can you use the invariance principle to estimate a and b separately given their combined form?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    The UK
    Posts
    5

    Re: Maximum likelihood estimation

    Well, could you explain it more please?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,879
    Thanks
    697

    Re: Maximum likelihood estimation

    The invariance principle says that if you have an estimate (say x for some parameter), then the estimation of a function of that parameter is f(x) if you use the MLE estimator.

    So if you have two estimators involving a and b are both from MLE estimators, then you can create a function that will calculate the estimate for that function.

    So if x = a - b and y = a + b then f(x,y) will get an MLE estimate for that function. So what functions can you create to isolate a and b if those estimations come from an MLE estimator?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2012
    From
    The UK
    Posts
    5

    Re: Maximum likelihood estimation

    I see what you mean, but (a+b) and (a-b) are not going to be a function they are just means for their distribution that I have written and their distributions are normal. If you just have a look again at the question, you would see what they are. But you have more experience anyway, just solve in any way that you think. Thank you very much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 23rd 2010, 03:20 AM
  2. [SOLVED] Maximum a posteriori estimation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 10th 2010, 06:37 AM
  3. Maximum Likelihood Estimation in Stata
    Posted in the Math Software Forum
    Replies: 0
    Last Post: May 6th 2010, 07:03 AM
  4. Maximum Likelihood estimation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 10th 2009, 01:46 PM
  5. Maximum Likelihood
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 20th 2009, 05:45 AM

Search Tags


/mathhelpforum @mathhelpforum