Monte Carlo-Based Covariance Matrix of Residuals and Critical Values in Minimum L1-Norm
| Autor: | Leonardo Castro de Oliveira, Sergio Baselga, Marcelo Tomio Matsuoka, Vinicius Francisco Rofatto, Ivandro Klein, Stefano Sampaio Suraci |
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| Rok vydání: | 2021 |
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Article Subject
010504 meteorology & atmospheric sciences Covariance matrix General Mathematics Computation Monte Carlo method 0211 other engineering and technologies General Engineering Estimator Contrast (statistics) 02 engineering and technology Expression (computer science) Engineering (General). Civil engineering (General) Residual 01 natural sciences Least squares QA1-939 Applied mathematics TA1-2040 Mathematics 021101 geological & geomatics engineering 0105 earth and related environmental sciences |
| Zdroj: | Mathematical Problems in Engineering, Vol 2021 (2021) |
| ISSN: | 1563-5147 1024-123X |
| DOI: | 10.1155/2021/8123493 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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