The problem of sequentially estimating powers of a scale parameter in a scale family and in a location-scale family is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under a scale invariant loss function and with the observation cost determined by a convex function of the stopping time and the number of observations up to that time.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-2,
author = {Agnieszka St\k epie\'n-Baran},
title = {Sequential estimation of powers of a scale parameter from delayed observations},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {13-28},
zbl = {1161.62046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-2}
}
Agnieszka Stępień-Baran. Sequential estimation of powers of a scale parameter from delayed observations. Applicationes Mathematicae, Tome 36 (2009) pp. 13-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-2/