Expansions for log densities of asymptotically normal estimates |
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| Authors: | Christopher S Withers Saralees Nadarajah |
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| Institution: | (1) Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA;(2) Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA;(3) Department of Statistics and Operations Research, Complutense University of Madrid, 28040 Madrid, Spain |
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| Abstract: | Edgeworth–type expansions are given for the log density and also for the derivatives of the density of an asymptotically normal
random variable having the standard expansions for its cumulants. Expansions for the log density are much simpler than for
the density. In fact the rth term of the expansion for the log density is a polynomial of degree only r + 2, while that for the density is a polynomial of degree 3r. |
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