Robust estimator for correlated observations based on bifactor equivalent weights

Yang, Yuanxi; Song, Lynda Jiwen; Xu, Tianhe

doi:10.1007/s00190-002-0256-7

Cited by 274 publications

(141 citation statements)

References 13 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…When weights of observations and correlations are incorporated into robust procedures, emphasis has been solely focused on efficiency, consistency and other asymptotic behaviours of robust estimators (see e.g. Gastwirth and Rubin 1975;Koul 1977;Portnoy 1977;Carroll and Ruppert 1982;Boente and Fraiman 1989;Xu 1989b;Yang et al 2002).…”

Section: The Effect Of Weights Of Observations On Robustnessmentioning

confidence: 99%

“…M-estimates have also been extended to correlated observations (see e.g. Gastwirth and Rubin 1975;Portnoy 1977;Boente and Fraiman 1989;Xu 1989b;Yang et al 2002) and to heterogenous models (Beran 1982;Carroll and Ruppert 1982). However, we may note that only the methods proposed by Xu (1989b) and Yang et al (2002) are generally applicable, since a particular structure of correlation has been presumed in the case of Gastwirth and Rubin (1975), Portnoy (1977) and Boente and Fraiman (1989).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

2005

J Geodesy

122

View full text Add to dashboard Cite

The findings of this paper are summarized as follows: (1) We propose a sign-constrained robust estimation method, which can tolerate 50% of data contamination and meanwhile achieve high, least-squares-comparable efficiency. Since the objective function is identical with least squares, the method may also be called sign-constrained robust least squares. An iterative version of the method has been implemented and shown to be capable of resisting against more than 50% of contamination. As a by-product, a robust estimate of scale parameter can also be obtained. Unlike the least median of squares method and repeated medians, which use a least possible number of data to derive the solution, the signconstrained robust least squares method attempts to employ a maximum possible number of good data to derive the robust solution, and thus will not be affected by partial near multicollinearity among part of the data or if some of the data are clustered together; (2) although M-estimates have been reported to have a breakdown point of 1/(t + 1), we have shown that the weights of observations can readily deteriorate such results and bring the breakdown point of M-estimates of Huber's type to zero. The same zero breakdown point of the L 1 -norm method is also derived, again due to the weights of observations; (3) by assuming a prior distribution for the signs of outliers, we have developed the concept of subjective breakdown point, which may be thought of as an extension of stochastic breakdown by Donoho and Huber but can be important in explaining real-life problems in Earth Sciences and image reconstruction; and finally, (4) We have shown that the least median of squares method can still break down with a single outlier, even if no highly concentrated good data nor highly concentrated outliers exist.

show abstract

Section: The Effect Of Weights Of Observations On Robustnessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

2005

J Geodesy

122

View full text Add to dashboard Cite

show abstract

“…is an attenuation function (e.g., Krarup and Kubik 1983;Yang 1994;Yang et al 2002). In such a case, the equivalent variance can be written as μ 2,i = μ 2,i /t (v i ).…”

Section: Theoretical Foundationsmentioning

confidence: 99%

M-estimation with probabilistic models of geodetic observations

Wiśniewski

2014

J Geod

View full text Add to dashboard Cite

The paper concerns M-estimation with probabilistic models of geodetic observations that is called M P estimation. The special attention is paid to M P estimation that includes the asymmetry and the excess kurtosis, which are basic anomalies of empiric distributions of errors of geodetic or astrometric observations (in comparison to the Gaussian errors). It is assumed that the influence function of M P estimation is equal to the differential equation that defines the system of the Pearson distributions. The central moments μ k , k = 2, 3, 4, are the parameters of that system and thus, they are also the parameters of the chosen influence function. The M P estimation that includes the Pearson type IV and VII distributions (M PD(l) method) is analyzed in great detail from a theoretical point of view as well as by applying numerical tests. The chosen distributions are leptokurtic with asymmetry which refers to the general characteristic of empirical distributions. Considering M-estimation with probabilistic models, the Gram-Charlier series are also applied to approximate the models in question (M G−C method). The paper shows that M P estimation with the application of probabilistic models belongs to the class of robust estimations; M PD(l) method is especially effective in that case. It is suggested that even in the absence of significant anomalies the method in question should be regarded as robust against gross errors while its robustness is controlled by the pseudo-kurtosis.

show abstract

“…The effects of gross errors to the estimator are eliminated through a properly built equivalent weight matrix [19]. Furthermore, variance components estimation is proposed for modifying the precision of observations from three types [16].…”

Section: Registration With the Gauss-helmert Modelmentioning

confidence: 99%

On the detection of systematic errors in terrestrial laser scanning data

Wang

Fang²

2012

Journal of Applied Geodesy

View full text Add to dashboard Cite

Abstract. Quality descriptions are parts of the key tasks of geodetic data processing. Systematic errors should be detected and avoided in order to insure the high quality standards required by structural monitoring. In this study, the iterative closest point (ICP) method was invested to detect systematic errors in two overlapping data sets. There are three steps to process the systematic errors: firstly, one of the data sets was transformed to a reference system by the introduction of the Gauss-Helmert (GH) model. Secondly, quadratic form estimation and segmentation methods are proposed to guarantee the overlapping data sets. Thirdly, the ICP method was employed for a finer registration and detecting the systematic errors. A case study was casted in which a dam surface in Germany was scanned by terrestrial laser scanning (TLS) technology. The results indicated that with the conjugation of ICP algorithm the accuracy of the data sets was improved approximately by 1.6 mm.

show abstract

Robust estimator for correlated observations based on bifactor equivalent weights

Cited by 274 publications

References 13 publications

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

M-estimation with probabilistic models of geodetic observations

On the detection of systematic errors in terrestrial laser scanning data

Contact Info

Product

Resources

About