Strategies admitting nonnegative unbiased variance estimators (Q1330221)

The work encompasses an interesting subject: uniformly nonnegative unbiased variance estimators of linear unbiased strategies for estimating population total. Before, \textit{J. N. K. Rao} and \textit{K. Vijayan} [J. Am. Stat. Assoc. 72, 579-584 (1977; Zbl 0369.62014)] had studied a similar problem, but they considered more specifically the strategy that consists of a Midzuno-Sen scheme and the ratio estimator. Strategies for which the natural unbiased variance estimators are uniformly nonnegative and those admitting uniformly nonnegative unbiased variance estimators are characterized. Several necessary and sufficient conditions for the nonnegatity of variance estimators vis-a-vis nonnegative definite matrices are given for quadratic variance estimators. On the other hand, a set of sufficient conditions for uniform nonnegativity of variance estimators is proposed. Finally, an algorithm to verify these conditions is given. The paper ends with a numerical example of this algorithm.