The case-deletion and mean-shift outlier models: equivalence and beyond

Deletion diagnostics have been widely adopted to evaluate the influence of one or more observations on the adjustment outputs. Both the case-deletion model and the mean-shift outlier model can be used to develop multiple case-deletion diagnostics for linear models. These two multiple outlier detection models are identical from the statistical point of view. However, the mean-shift outlier model, in which the underlying observations are implicitly deleted, outweighs the case-deletion model in term of computational efficiency. The influence of outliers on the adjustment outputs is also addressed. It reveals that the precision, minimal detectable bias (MDB) measure and dilution of precision metric (DOP) are all overestimated when outliers exist but were neglected under the assumption that a priori variance factor is known before.

[1]  J. Simonoff,et al.  Procedures for the Identification of Multiple Outliers in Linear Models , 1993 .

[2]  Sergio Baselga.  Exhaustive search procedure for multiple outlier detection , 2011 .

[3]  G. Strang,et al.  Linear Algebra, Geodesy, and GPS , 1997 .

[4]  John Law,et al.  Robust Statistics—The Approach Based on Influence Functions , 1986 .

[5]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[6]  C. Ghilani,et al.  Adjustment Computations: Statistics and Least Squares in Surveying and GIS , 1987 .

[7]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[8]  D. Monhor,et al.  Further remarks on the concept of outlier with particular relevance to the valuable outliers , 2011 .

[9]  Burkhard Schaffrin,et al.  Three-dimensional outlier detection for GPS networks and their densification via the BLIMPBE approach , 2003 .

[10]  Jikun Ou,et al.  Quasi-Accurate Detection of Outliers for Correlated Observations , 2007 .

[11]  Burkhard Schaffrin,et al.  Reliability Measures for Correlated Observations , 1997 .

[12]  D. Monhor,et al.  Understanding the concept of outlier and its relevance to the assessment of data quality: Probabilistic background theory , 2005 .

[13]  Karl-Rudolf Koch,et al.  Parameter estimation and hypothesis testing in linear models , 1988 .

[14]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[15]  W. Baarda,et al.  A testing procedure for use in geodetic networks. , 1968 .

[16]  R. Cook.  Influential Observations in Linear Regression , 1979 .

[17]  S. Hekimoglu,et al.  A new outlier detection method considering outliers as model errors , 2015, Experimental Techniques.

[18]  S. Chatterjee.  Sensitivity analysis in linear regression , 1988 .

[19]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[20]  J. Ou,et al.  Reliability Analysis for a Robust M-Estimator , 2011 .