Estimation of Fisher information using model selection |
| |
Authors: | Jan Mielniczuk Ma?gorzata Wojty? |
| |
Institution: | 1. Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland 2. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland
|
| |
Abstract: | In the paper the problem of estimation of Fisher information I
f
for a univariate density supported on 0, 1] is discussed. A starting point is an observation that when the density belongs
to an exponential family of a known dimension, an explicit formula for I
f
there allows for its simple estimation. In a general case, for a given random sample, a dimension of an exponential family
which approximates it best is sought and then estimator of I
f
is constructed for the chosen family. As a measure of quality of fit a modified Bayes Information Criterion is used. The
estimator, which is an instance of Post Model Selection Estimation method is proved to be consistent and asymptotically normal
when the density belongs to the exponential family. Its consistency is also proved under misspecification when the number
of exponential models under consideration increases in a suitable way. Moreover we provide evidence that in most of considered
parametric cases the small sample performance of proposed estimator is superior to that of kernel estimators. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|