Systematic bias of selected estimates applied in vertical displacement analysis

Abstract

Abstract In surveying problems we almost always use unbiased estimators; however, even unbiased estimator might yield biased assessments, which is due to data. In statistics one distinguishes several types of such biases, for example, sampling, systemic or response biases. Considering surveying observation sets, bias from data might result from systematic or gross errors of measurements. If nonrandom errors in an observation set are known, then bias can easily be determined for linear estimates (e.g., least squares estimates). In the case of non-linear estimators, it is not so simple. In this paper we are focused on a vertical displacement analysis and we consider traditional least squares estimate, two M split estimates and two basic robust estimates, namely M-estimate, R-estimate. The main aim of the paper is to assess estimate biases empirically by applying Monte Carlo method. The smallest biases are obtained for M- and R-estimates, especially for a high magnitude of a gross error. On the other hand, there are several cases when M split estimates are the best. Such results are acquired when the magnitude of a gross error is moderate or small. The outcomes confirm that bias of M split estimates might vary for different point displacements.