The influence function of the Stahel–Donoho covariance estimator of smallest outlyingness

M. Debruyne; M. Hubert

doi:10.1016/j.spl.2008.08.006

The influence function of the Stahel–Donoho covariance estimator of smallest outlyingness

Statistics & Probability Letters ◽

10.1016/j.spl.2008.08.006 ◽

2009 ◽

Vol 79 (3) ◽

pp. 275-282 ◽

Cited By ~ 16

Author(s):

M. Debruyne ◽

M. Hubert

Keyword(s):

Influence Function ◽

Covariance Estimator

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An improved methodology for applying the influence function for subsidence hazard prediction

Georisk Assessment and Management of Risk for Engineered Systems and Geohazards ◽

10.1080/17499518.2021.1875247 ◽

2021 ◽

pp. 1-13

Author(s):

Ali Saeidi ◽

Olivier Deck ◽

Mahdiyeh Seifaddini ◽

Marwan A. L. Heib ◽

Thierry Verdel

Keyword(s):

Influence Function

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Influence Function based Data Poisoning Attacks to Top-N Recommender Systems

Proceedings of The Web Conference 2020 ◽

10.1145/3366423.3380072 ◽

2020 ◽

Cited By ~ 3

Author(s):

Minghong Fang ◽

Neil Zhenqiang Gong ◽

Jia Liu

Keyword(s):

Recommender Systems ◽

Influence Function

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Explaining the rural-urban learning achievements gap in Ethiopian primary education: a re-centered influence function decomposition using Young Lives data

Education Economics ◽

10.1080/09645292.2021.1872504 ◽

2021 ◽

pp. 1-29

Author(s):

Jean-Baptiste M.B. Sanfo ◽

Keiichi Ogawa

Keyword(s):

Primary Education ◽

Influence Function ◽

Function Decomposition ◽

Young Lives

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Correlation between influence-function quality and predictability of a computer-controlled polishing process

Optical Engineering ◽

10.1117/1.2213630 ◽

2006 ◽

Vol 45 (6) ◽

pp. 063401 ◽

Cited By ~ 2

Author(s):

Elmar Pitschke

Keyword(s):

Influence Function ◽

Polishing Process ◽

Computer Controlled

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A local trust model based on time influence function in P2P networks

2015 6th IEEE International Conference on Software Engineering and Service Science (ICSESS) ◽

10.1109/icsess.2015.7339108 ◽

2015 ◽

Cited By ~ 1

Author(s):

Yan-xia Cui ◽

Hong-yun Ning ◽

Yun-yun Du

Keyword(s):

Influence Function ◽

Trust Model ◽

P2p Networks ◽

Model Based

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The influence function of penalized regression estimators

Statistics ◽

10.1080/02331888.2014.922563 ◽

2014 ◽

Vol 49 (4) ◽

pp. 741-765 ◽

Cited By ~ 9

Author(s):

Viktoria Öllerer ◽

Christophe Croux ◽

Andreas Alfons

Keyword(s):

Influence Function ◽

Penalized Regression ◽

Regression Estimators

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Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

Journal of Navigation ◽

10.1017/s0373463311000415 ◽

2011 ◽

Vol 64 (S1) ◽

pp. S3-S18 ◽

Cited By ~ 20

Author(s):

Yuanxi Yang ◽

Jinlong Li ◽

Junyi Xu ◽

Jing Tang

Keyword(s):

Least Squares ◽

Stochastic Models ◽

Influence Function ◽

A Priori ◽

Functional Model ◽

Global Navigation Satellite Systems ◽

Parameter Estimates ◽

Model Parameters ◽

Integrated Navigation ◽

Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

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