Here's a little question for time series/robustness experts:
Under `mild conditions' on the autocorrelations, the variance
of the average of a time series of length $n$ is $O(n^{-1})$,
i.e. of form $a/n$ for large $n$. Is any corresponding
result known for the median of the series?
(If the data were white noise, the answer would be that
the variance of the median is also $O(n^{-1})$. Does
the presence of autocorrelation have a dramatic effect?)
Hints, insight and references all very welcome, but
please reply to me and not to allstat.
I'll post a summary of replies.
Thanks.
--
Professor A. C. Davison
Department of Mathematics
Swiss Federal Institute of Technology Lausanne
CH-1015 Lausanne EPFL
Switzerland Tel: + 41 (0)21 693
5502
Sec: + 41 (0)21 693 2565
http://statwww.epfl.ch/ Fax: + 41 (0)21 693 4250
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