Posted on Wednesday, 29th February 2012

Please read the rest of Chapter 8 and post a comment.

Posted in Class | Comments (13)

  1. Yijuan Du Says:
    February 29th, 2012 at 8:05 pm

    What is the practical importance of Fisher information?

  2. Eric VanEpps Says:
    February 29th, 2012 at 8:58 pm

    Could we go through how the standard error is calculated from the second derivative of the loglikelihood function? I’m still not entirely comfortable with the loglikelihood function, and going through an extended example would really clarify those notes for me. Thanks.

  3. Shubham Debnath Says:
    February 29th, 2012 at 11:20 pm

    Is there a relationship between the Hessian of a matrix and its discriminant, perhaps at a particular theta? If so, is there any statistical significance in the discriminant?

  4. nsnyder Says:
    February 29th, 2012 at 11:35 pm

    In 8.4.4 the warning regarding application of numerical maximization to ML estimation is brought up with the concern of relative maxima in the loglikelihood. Is this only the case if the data is not from a normal distribution? Do these maxima correspond to anything interesting about the data?

  5. Jay Scott Says:
    March 1st, 2012 at 12:38 am

    In 8.4.4 p241 you speak of multiple local maxima in loglikelihood causing numerical methods of estimating ML to get stuck in a region other than the actual maximum. Is there a rule of thumb for determining when this will be a problem? Is there a method for flattening the curve to reduce local variation yet still get a good estimate of ML?

  6. Rex Tien Says:
    March 1st, 2012 at 12:53 am

    It is shown that the MLE of the standard deviation is not equal to the common standard deviation formula. Can you explain more why we want to depart from MLE in this case? And are there other concrete examples when it is preferable to stray from MLE?

  7. Matt Panico Says:
    March 1st, 2012 at 1:50 am

    I’m having trouble thinking of a situation in which a method of estimation would not be invariant to transformations of the parameter. If the actual parameter is transformed, why wouldn’t its estimate be transformed in the same way?

  8. Kelly Says:
    March 1st, 2012 at 2:17 am

    I read through the section on Fisher information several times and am still confused about its meaning and derivation. Also, is it only related to estimators, or does it relate somehow to observed data as well?

  9. David Zhou Says:
    March 1st, 2012 at 3:12 am

    What is the origin of using partial differentiation for maximum likelihood estimation? In addition to the math, I’m interested in the significance of this method.

    Can you talk some more about the mathematical care that needs to go into maximum likelihood estimation?

  10. Scott Kennedy Says:
    March 1st, 2012 at 8:08 am

    When would I use the loglikelihood function instead of the methods in Chapter 7 to find the standard error? And vice versa?

  11. Amanda Markey Says:
    March 1st, 2012 at 8:37 am

    I’m still not clear on the concept of efficiency – is it a measure of whether the variance of the estimator is bounded?

    Also, does the concept of efficiency relate to the following statement (and if so, how?): it is sometimes better to take a biased estimator over an unbiased estimator if the sampling variance of the unbiased estimator is sufficiently smaller.

  12. Rich Truncellito Says:
    March 1st, 2012 at 9:22 am

    Because the inverse of I(θ) may be equated to V(T), it seems that √[I(θ)]•(θ^ – θ) may be a rephrasing of the statistic ratio (θ^ – θ)/SE(θ^) in chapter 10. Is assuming this apparent relationship accurate?

  13. Thomas Kraynak Says:
    March 1st, 2012 at 9:24 am

    When estimating parameters using ML in software, what are the number of iterations needed for making an efficient estimator?

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