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Jacobian Matrix of Residuals

  1. Sep 15, 2011 #1
    There are 2 parameters in the Gamma distribution, alpha and beta. If sample 500 of the Gamma random variable, there unbiased mean and variance can be estimated by the sample moments.

    If it is also interested to estimate the variance and covariance of the parameters, alpha and beta; Jacobian matrix of residuals has to be defined, Jr. There fore the covariance matrix is:

    inverse(transpose(Jr)residual)sample variance

    I want to know about the calculation of the Jacobian matrix of residuals.
     
  2. jcsd
  3. Sep 16, 2011 #2

    Stephen Tashi

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    Do you mean "the variance and covariance of the estimators of the parameters"? The parameters themselves are constant, they don't have a variance.
     
  4. Sep 16, 2011 #3
    Yes, I should stated more clearly. How to do the covariance of the estimators? I use too much simulation methods, this kind exact formulation I did not work with before.
     
  5. Sep 16, 2011 #4

    Stephen Tashi

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