### Szczegóły

#### Tytuł artykułu

Empirical tests of performance of some M – estimators#### Tytuł czasopisma

Geodesy and Cartography#### Rocznik

2014#### Wolumin

vol. 63#### Numer

No 2#### Autorzy publikacji

#### Słowa kluczowe

M – estimation ; iteratively reweighted least squares ; tuning constant ; outliers ; network adjustment#### Wydział PAN

Nauki Techniczne#### Abstrakt

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.#### Wydawca

Commitee on Geodesy PAS#### Data

2014#### Typ

Artykuły / Articles#### Identyfikator

ISSN 2080-7636#### DOI

10.2478/geocart-2014-0010