Estimating the total of a continuous population
A continuous population on the real line may be considered as the realization y(t) of a random process Y(t) with a trend function and a covariance function. On the basis of sample values \(y(t_ 1),...,y(t_ n)\) it is natural to choose the estimator \(\hat T\) of the toal \(T=\int^{a}_{0}y(t)dt\) so that \(E[(\hat T-T)^ 2]\) is minimized. Various criteria for choosing the sample ofpoints and the estimator are discussed in this paper. One result is that for a constant trend and triangular covariance function \(\gamma (t)=C\cdot (1-| t| /a)\), the centered systematic sample and \(\hat T=a\sum y(t_ i)/n\) provide the optimal choice. A similar result is also given for the case of a quadratic trend.
scientific article; zbMATH DE number 3974034