Fisher Information of Scale

Details Fisher Information of Scale Fisher Information of Scale

2010-05-06

arxiv.org/abs/1005.0983v3

Statistics and Probability Letters 80 (2010), pp. 1881-1885

Mathematics

Statistics Theory

6 pages

Scientific paper

10.1016/j.spl.2010.08.015

Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as a suitable supremum. In addition, we enforce equivariance by a scale factor. Fisher information of scale is weakly lower semicontinuous and convex. It is finite iff the usual assumptions on densities hold, under which Fisher information of scale is classically defined, and then both classical and our notions agree. Fisher information of scale finite is also equivalent to L_2-differentiability and local asymptotic normality, respectively, of the scale model induced by F.

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