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A Strong Representation for Linear Combinations of Order Statistics with Application to Fixed-Width Confidence Intervals for Location and Scale Parameters
Ist Teil von
Scandinavian journal of statistics, 1983-01, Vol.10 (2), p.97-115
Ort / Verlag
Oxford: Almqvist & Wiksell Periodical Co
Erscheinungsjahr
1983
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
A class of linear combinations of order statistics (LCOSs) based on a random sample drawn from an arbitrary distribution is represented as a sum of independent and identically distributed random variables plus a remainder term which tends to zero almost-surely (a.s.) at a certain rate. A general sequential method of constructing fixed-width confidence intervals for the location parameter of a distribution is given and its asymptotic properties are studied. This constitutes a generalization of the results of Chow & Robbins (1965). These results are used to construct fixed-width confidence interval procedures for the location parameter and fixed-diameter confidence ellipse procedures for both location and scale parameters when the point estimates are based on LCOSs. As a by-product, an invariance principle is obtained for LCOSs.