Linear estimation of location and scale parameters using partial maxima
Date
2012Author
Papadatos, NickosSource
MetrikaVolume
75Issue
2Pages
243-270Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
Consider an i. i. d. sample X 1*, X 2*,..., X n*, from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima) sequence, X 1:1*,X 2:2*,..., X n:n*, where X j:j* = max{X 1*,..., X j*} This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd's (in Biometrica 39:88-95, 1952) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/ log n), for a wide class of distributions. © 2010 Springer-Verlag.