@ARTICLE{Banaś_Marek_Empirical_2014,
 author={Banaś, Marek and Ligas, Marcin},
 volume={vol. 63},
 number={No 2},
 journal={Geodesy and Cartography},
 howpublished={online},
 year={2014},
 publisher={Polska Akademia Nauk/ Komitet Geodezji Polskiej Akademii Nauk; Polish Academy of Sciences / Commitee on Geodesy Polish Academy of Sciences},
 abstract={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.},
 type={Artykuły / Articles},
 title={Empirical tests of performance of some M – estimators},
 URL={http://ochroma.man.poznan.pl/Content/98355/PDF/art1_Banas_ligas.pdf},
 doi={10.2478/geocart-2014-0010},
 keywords={M – estimation, iteratively reweighted least squares, tuning constant, outliers, network adjustment},
}