Precomputing Influences of Observation for a Network

Abstract

Formulae for judging a priori the influences of individual observations on the unknown parameters and the mean network precision are presented. The influences of an observation on the parameters and the mean network precision are measured by the influence index and the percentage share, respectively. The larger the redundancy number, or the smaller the parameter number of the observation, the smaller the influence index will be and hence the less influence the observation will have on the estimate of an unknown parameter vector. A larger parameter number ensures a high percentage share in the mean network precision. The numerical example of the first-order leveling network of Taiwan seems to indicate that a better weighting scheme tends to produce more homogeneities among the individual parameter numbers and their corresponding influence numbers.