Details

Title

Empirical tests of performance of some M – estimators

Journal title

Geodesy and Cartography

Yearbook

2014

Volume

vol. 63

Numer

No 2

Publication authors

Keywords

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

Divisions of PAS

Nauki Techniczne

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.

Publisher

Commitee on Geodesy PAS

Date

2014

Type

Artykuły / Articles

Identifier

ISSN 2080-7636

DOI

10.2478/geocart-2014-0010

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