A1 - Banaś, Marek
A1 - Ligas, Marcin
PB - Commitee on Geodesy PAS
N2 - The paper presents an empirical comparison of performance of three well
known M – estimators (i.e. Huber, Tukey and Hampel’s M – estimators) and also some
new ones. The new M – estimators were motivated by weighting functions applied in
orthogonal polynomials theory, kernel density estimation as well as one derived from
Wigner semicircle probability distribution. M – estimators were used to detect outlying
observations in contaminated datasets. Calculations were performed using iteratively
reweighted least-squares (IRLS). Since the residual variance (used in covariance matrices
construction) is not a robust measure of scale the tests employed also robust measures i.e.
interquartile range and normalized median absolute deviation. The methods were tested
on a simple leveling network in a large number of variants showing bad and good sides
of M – estimation. The new M – estimators have been equipped with theoretical tuning
constants to obtain 95% efficiency with respect to the standard normal distribution. The
need for data – dependent tuning constants rather than those established theoretically is
also pointed out.
KW - M – estimation
KW - iteratively reweighted least squares
KW - tuning constant
KW - outliers
KW - network adjustment
T1 - Empirical tests of performance of some M – estimators