By James W. Hardin, Joseph M. Hilbe

ISBN-10: 1584883073

ISBN-13: 9781584883074

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G. 60) 0{3 ( ) may be estimated as (the (the inverse inverse of) of) the the usual estimate of variance based based on on may be estimated as usual estimate of variance the information matrix VH-a naive variance estimate assuming the data are the information matrix VH-a naive variance estimate assuming the data are from distribution distribution f. f. Cases Cases which which allow allow swapping swapping of of the the order order of of expectation expectation from and differentiation are validated through convergence theorems not covered in in differentiation and are validated through convergence theorems not covered this text.

Where Ti(xi,,3) For likelihood-based models, models, the the estimating equation is is the the derivative derivative For our our likelihood-based estimating equation ofthe log-likelihood for for the the distribution, distribution, Of o£/oj3. Our desire is to to evaluate evaluate the the of the log-likelihood desire is 10,3 . Our © © 2003 2003 by by Chapman Chapman & & Hall/CRC Hall/CRC ESTIMATING THE VARIANCE VARIANCE OF OF THE THE ESTIMATES ESTIMATES ESTIMATING THE 29 29 properties of the variance variance estimate estimate for for cases cases when when the the data data really really come come from from properties of the distribution distribution g.

Case of of uit The Uit values are the scores. The uit values are the scores . that the the middle middle of of the the modified sandwich estimate estimate of of variance variance We emphasize emphasize that We modified sandwich has replaced panels panels of of observations observations with with their their respective respective sums. sums. The rank of of has replaced The rank © © 2003 2003 by by Chapman Chapman & & Hall/CRC Hall/CRC ESTIMATING THE VARIANCE VARIANCE OF OF THE THE ESTIMATES ESTIMATES ESTIMATING THE 31 31 the resulting matrix is is less less than than the the number number of of panels panels in in the the construction construction..

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