TY - JOUR
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.
L1 - http://journals.pan.pl/Content/98355/PDF/art1_Banas_ligas.pdf
L2 - http://journals.pan.pl/Content/98355
PY - 2014
IS - No 2
DO - 10.2478/geocart-2014-0010
KW - M – estimation
KW - iteratively reweighted least squares
KW - tuning constant
KW - outliers
KW - network adjustment
A1 - Banaś, Marek
A1 - Ligas, Marcin
PB - Commitee on Geodesy PAS
VL - vol. 63
DA - 2014
T1 - Empirical tests of performance of some M – estimators
UR - http://journals.pan.pl/dlibra/publication/edition/98355
T2 - Geodesy and Cartography
ER -