Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search

Koch, Ismael É.; Klein, Ivandro; Gonzaga, Luiz; Matsuoka, Marcelo Tomio; Rofatto, Vinicius Francisco; Veronez, Maurício Roberto

doi:10.3390/s19204535

Cited by 8 publications

(2 citation statements)

References 48 publications

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“…Classes of this technique include M-estimates (which follow from maximum likelihood considerations), L-Estimates (which are linear combinations of order statistics), and R-Estimates (based on statistical rank tests). Some classes of such robust adjustment methods, as well as their properties, are well known, while other methods are still being researched (see, e.g., L 1 -norm estimation [24], M-estimation [25][26][27], R-estimation [28][29][30] and those based on meta-heuristics [31]). Besides the undoubted advantages of Robust Estimation, here, we focus on the hypothesis test-based outlier.…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

et al. 2020

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An iterative outlier elimination procedure based on hypothesis testing, commonly known as Iterative Data Snooping (IDS) among geodesists, is often used for the quality control of modern measurement systems in geodesy and surveying. The test statistic associated with IDS is the extreme normalised least-squares residual. It is well-known in the literature that critical values (quantile values) of such a test statistic cannot be derived from well-known test distributions but must be computed numerically by means of Monte Carlo. This paper provides the first results on the Monte Carlo-based critical value inserted into different scenarios of correlation between outlier statistics. From the Monte Carlo evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, over-identifications and statistical overlap associated with IDS in the presence of a single outlier. On the basis of such probability levels, we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for cases in which IDS is in play. The MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances in which the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection but the lower the rates of outlier identification. In such a case, the larger the Type I Error, the larger the ratio between the MIB and MDB. We also highlight that an outlier becomes identifiable when the contributions of the measures to the wrong exclusion rate decline simultaneously. In this case, we verify that the effect of the correlation between outlier statistics on the wrong exclusion rate becomes insignificant for a certain outlier magnitude, which increases the probability of identification.

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Section: Introductionmentioning

confidence: 99%

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

et al. 2020

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“…However, if there are outliers in the sample, the LS will provide biased parameters [2,3]. Here, we follow the definition of Lehmann [4]: "an outlier is an observation that is so probably caused by a gross error that it is better not used or not used as it is."…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo-Based Covariance Matrix of Residuals and Critical Values in Minimum L1-Norm

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Oliveira

Klein

et al. 2021

Mathematical Problems in Engineering

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Robust estimators are often lacking a closed-form expression for the computation of their residual covariance matrix. In fact, it is also a prerequisite to obtain critical values for normalized residuals. We present an approach based on Monte Carlo simulation to compute the residual covariance matrix and critical values for robust estimators. Although initially designed for robust estimators, the new approach can be extended for other adjustment procedures. In this sense, the proposal was applied to both well-known minimum L1-norm and least squares into three different leveling network geometries. The results show that (1) the covariance matrix of residuals changes along with the estimator; (2) critical values for minimum L1-norm based on a false positive rate cannot be derived from well-known test distributions; (3) in contrast to critical values for extreme normalized residuals in least squares, critical values for minimum L1-norm do not necessarily tend to be higher as network redundancy increases.

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