Simplified algebraic estimation for the quality control of DIA estimator

Yang, Ling; Shen, Yunzhong; Li, Bofeng; Rizos, Chris

doi:10.1007/s00190-020-01454-9

Cited by 29 publications

(11 citation statements)

References 23 publications

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“…In the following discussion, the DIA probability levels (Teunissen 2018;Zaminpardaz and Teunissen 2019;Yang et al 2021) are used to evaluate the performance of IDS and IDR, which can be calculated via MCS (Hekimoglu and Koch 1999;Rofatto et al 2020b). Specifically, when there is no outlier, P FA denotes the probability of false alarm (FA) for rejecting any inlier.…”

Section: Examplementioning

confidence: 99%

An extended w-test for outlier diagnostics in linear models

Yu,

Yang,

Shen

2024

Preprint

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The issue of outliers has been a research focus in the field of geodesy. Based on a statistical testing method known as the w-test, data snooping along with its iterative form, iterative data snooping (IDS), is commonly used to diagnose outliers in linear models. However, in the case of multiple outliers, it may suffer from the masking and swamping effects, thereby limiting the detection and identification capabilities. This contribution is to investigate the cause of masking and swamping effects and to propose a new method to mitigate these phenomena. First, based on the data division, an extended form of the wtest with its reliability measure is proposed, and a theoretical reinterpretation of data snooping and IDS is provided. Then, to alleviate the effects of masking and swamping, a new outlier diagnostic method and its iterative form are presented, namely data refining and iterative data refining (IDR). In general, if the total observations are initially divided into an inlying set and an outlying set, data snooping can be considered a process of selecting outliers from a preset inlying set to the outlying set. In contrast, data refining is then a reverse process to transfer inliers from an outlying set to the inlying one. Both theoretical analysis and application examples show that IDR would keep stronger robustness than IDS due to the alleviation of masking and swamping effect, although it may pose a higher risk of precision loss when dealing with insufficient data.

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Section: Examplementioning

confidence: 99%

An extended w-test for outlier diagnostics in linear models

Yu,

Yang,

Shen

2024

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Examplementioning

confidence: 99%

An extended w-test for outlier diagnostics in linear models

Yu,

Yang,

Shen

2023

Preprint

Self Cite

View full text Add to dashboard Cite

The issue of dealing with outliers has been a research focus in the field of geodesy. Based on the statistical testing method known as the w-test, data snooping along with its iterative form, iterative data snooping (IDS), is commonly used to diagnose outliers in linear models. However, in the case of multiple outliers, these methods may suffer from the masking and swamping effects, thereby limiting their detection and identification capabilities. This contribution is to investigate the cause of masking and swamping effects and to propose a new method to mitigate these phenomena. First, based on the data division, an extended form of the w-test with its reliability measure is proposed, and a theoretical reinterpretation of data snooping and IDS is provided. Then, to alleviate the effects of masking and swamping, a new outlier diagnostic method and its iterative form are presented, namely data refining and iterative data refining (IDR). In general, if the total observations are initially divided into an inlying set and an outlying set, data snooping can be considered a process of selecting outliers from a preset inlying set to the outlying set. In contrast, data refining is then a reverse process to transfer inliers from an outlying set to the inlying one. Both theoretical analysis and actual application examples show that IDR would keep stronger robustness than IDS due to the alleviation of masking and swamping effect, although it may pose a higher risk of accuracy loss when dealing with insufficient data.

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“…where B ∈ R m×r is a matrix of rank(B) = r , such that [A B] ∈ R m×m is invertible and A T B = 0, see, e.g., (Yang et al 2021;Teunissen 2003, p. 62) for constructing matrix B.…”

Section: Integrated Estimation and Testingmentioning

confidence: 99%

On the computation of confidence regions and error ellipses: a critical appraisal

Zaminpardaz

Teunissen

2022

J Geod

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Customary confidence regions do not truly reflect in the majority of our geodetic applications the confidence one can have in one’s produced estimators. As it is common practice in our daily data analyses to combine methods of parameter estimation and hypothesis testing before the final estimator is produced, it is their combined uncertainty that has to be taken into account when constructing confidence regions. Ignoring the impact of testing on estimation will produce faulty confidence regions and therefore provide an incorrect description of estimator’s quality. In this contribution, we address the interplay between estimation and testing and show how their combined non-normal distribution can be used to construct truthful confidence regions. In doing so, our focus is on the designing phase prior to when the actual measurements are collected, where it is assumed that the working (null) hypothesis is true. We discuss two different approaches for constructing confidence regions: Approach I in which the region’s shape is user-fixed and only its size is determined by the distribution, and Approach II in which both the size and shape are simultaneously determined by the estimator’s non-normal distribution. We also prove and demonstrate that the estimation-only confidence regions have a poor coverage in the sense that they provide an optimistic picture. Next to the provided theory, we provide computational procedures, for both Approach I and Approach II, on how to compute confidence regions and confidence levels that truthfully reflect the combined uncertainty of estimation and testing.

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Simplified algebraic estimation for the quality control of DIA estimator

Cited by 29 publications

References 23 publications

An extended w-test for outlier diagnostics in linear models

An extended w-test for outlier diagnostics in linear models

An extended w-test for outlier diagnostics in linear models

On the computation of confidence regions and error ellipses: a critical appraisal

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