Robust estimation in the simple errors-in-variables model

Fekri, M.; Ruiz‐Gazen, Anne

doi:10.1016/j.spl.2006.04.015

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…In other cases, a comparison is desirable between two non‐direct techniques such as CRS and an optical level or laser scanner. In these cases, both sets of coordinate estimates can be anticipated to be affected by errors, and a Type I regression can no longer be assumed as an appropriate statistical model to relate them (Fekri and Ruiz‐Gazen, 2006). Alternatively, an EVM procedure (regression Type II) is appropriate, where both the CRS and the direct measurements are considered as dependent.…”

Section: Discussionmentioning

confidence: 99%

Close Range Stereophotogrammetry and Video Imagery Analyses in Soil Ecohydrology Modelling

Rossi¹,

Ares²

2012

The Photogrammetric Record

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Ecohydrology is an emerging discipline in the environmental sciences. Soil micro‐relief is of relevance to various ecohydrological processes such as rainwater redistribution, seed displacement through water runoff, water erosion and plant competition for water. Mechanical–optical methods to characterise the soil surface and its incidence in these processes are time consuming and can produce modifications of soil relief. This research explores a methodology combining non‐contact techniques (close range stereophotogrammetry and geostatistical modelling) for microtopographic description with video imagery analysis to formulate quantitative determination of surface water movement and infiltration in undisturbed field plots. The numerical quality of the results obtained was tested with ad hoc laboratory models representing various elementary landforms (basin, hill and ridge), as well as with infiltration runoff experiments in undisturbed field plots. The requirements to define a minimum set of properly oriented digital images to attain target precision thresholds in modelling soil microtopography for ecohydrological applications are shown as well as the conditions and experimental arrangement to obtain adequate video imagery of water movement on the soil surface. The use of geostatistical algorithms to analyse ecohydrological processes occurring at the soil surface is illustrated with results obtained from field plots. The methodology presented serves to characterise and quantify water‐related ecological processes occurring at the soil surface while preserving undisturbed soil conditions. Potential applications are in ecohydrology, soil erosion science and environmental material transport studies.

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Section: Discussionmentioning

confidence: 99%

Close Range Stereophotogrammetry and Video Imagery Analyses in Soil Ecohydrology Modelling

Rossi¹,

Ares²

2012

The Photogrammetric Record

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“…Fekri and Ruiz‐Gazen (2004) and Fekri and Ruiz‐Gazen (2006) derived limiting distributions of the robust MA estimators in the context of errors‐in‐variables models. In this section we will review their results and extend them to the case of robust SMA estimators.…”

Section: Robust Estimation and Inference In Allometrymentioning

confidence: 99%

“…The influence functions and asymptotic distributions of the proposed MA estimators were also given. In Fekri and Ruiz‐Gazen (2006), robust slope estimators were considered in simple errors‐in‐variance models with other error variance assumptions. In the principal component analysis literature, robust covariance estimators have been considered by Devlin et al (1981) by means of M ‐estimators.…”

Section: Introductionmentioning

confidence: 99%

Robust estimation and inference for bivariate line-fitting in allometry

Taskinen

Warton

2011

Biom. J.

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In allometry, bivariate techniques related to principal component analysis are often used in place of linear regression, and primary interest is in making inferences about the slope. We demonstrate that the current inferential methods are not robust to bivariate contamination, and consider four robust alternatives to the current methods -- a novel sandwich estimator approach, using robust covariance matrices derived via an influence function approach, Huber's M-estimator and the fast-and-robust bootstrap. Simulations demonstrate that Huber's M-estimators are highly efficient and robust against bivariate contamination, and when combined with the fast-and-robust bootstrap, we can make accurate inferences even from small samples.

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