Empirical influence functions and their non-standard applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Duchnowski ◽  
Patrycja Wyszkowska
Keyword(s):  
Outlier Detection ◽  
Influence Function ◽  
Statistical Tests ◽  
Influence Functions ◽  
Robust Methods ◽  
General Properties ◽  
Gross Error

Abstract The main objective of the empirical influence function (EIF) is to describe how estimates behave when an observation set is affected by gross errors. Unlike the influence function, which represents the estimation method’s general properties, EIF can provide valuable information about applying different methods to a particular network. The chosen example allows us to compare different robust methods. The paper focuses on non-standard applications of EIF, for example, in assuming steering parameter of robust methods (usually related to the assumed interval for acceptable observation errors). The paper shows that commonly used values do not always work well, and EIFs might help choose appropriate values, guaranteeing the estimation process’s robustness. The most important new application of EIFs concerns the detection and assessment of a single gross error. The blinded experiments proved that such an approach is correct and can be an alternative to classic statistical tests for outlier detection.

On transformation strains and uniform fields in multiphase elastic media

1992 ◽  
Vol 437 (1900) ◽  
pp. 291-310 ◽  
Keyword(s):  
Concentration Factor ◽  
Elastic Stiffness ◽  
Local Fields ◽  
Influence Functions ◽  
Elastic Solids ◽  
Two Phase ◽  
General Properties ◽  
Multiphase Systems ◽  
Concentration Factors ◽  
Mechanical Influence

The effect of local eigenstrain and eigenstress fields, or transformation fields, on the local strains and stresses is explored in multiphase elastic solids of arbitrary geometry and material symmetry. The residual local fields caused by such transformation fields are sought in terms of certain transformation influence functions and transformation concentration factor tensors. General properties of these functions and concentration factors, and their relation to the analogous mechanical influence functions and concentration factors, are established, in part, with the help of uniform strain fields in multiphase media. Specific estimates of the transformation concentration factor tensors are evaluated by the self-consistent and Mori-Tanaka methods. It is found here that although the two methods use different constraint tensors in solutions of the respective dilute problems, their estimates of the mechanical, thermal, and transformation concentration factor tensors, and of the overall stiffness of multiphase media have a similar structure. Proofs that guarantee that these methods comply with the general properties of the transformation influence functions, and provide diagonally symmetric estimates of the overall elastic stiffness, are given for two-phase and multiphase systems consisting of, or reinforced by, inclusions of similar shape and alignment. One of the possible applications of the results, in analysis of overall instantaneous properties and local fields in inelastic composite materials, is described in the following paper.

scholarly journals Preferences and Social Influence

2018 ◽  
Vol 10 (3) ◽  
pp. 124-142 ◽  
Author(s):  
Chaim Fershtman ◽  
Uzi Segal
Keyword(s):  
Social Influence ◽  
Influence Function ◽  
Decision Makers ◽  
Influence Functions ◽  
Group Decisions ◽  
Equilibrium Behavior ◽  
Behavioral Preferences

Interaction between decision makers may affect their preferences. We consider a setup in which each individual is characterized by two sets of preferences: his unchanged core preferences and his behavioral preferences. Each individual has a social influence function that determines his behavioral preferences given his core preferences and the behavioral preferences of other individuals in his group. Decisions are made according to behavioral preferences. The paper considers different properties of these social influence functions and their effect on equilibrium behavior. (JEL D11, D83, D91, Z13)

Influence Functions in the Numerical Analysis of Bending of Thin Elastic Plates

1984 ◽  
Vol 8 (2) ◽  
pp. 103-114 ◽  
Author(s):  
Mohammed F.N. Mohsen ◽  
Ali A. Al-Gadhib ◽  
Mohammed H. Baluch
Keyword(s):  
Boundary Conditions ◽  
Influence Function ◽  
Infinite Plate ◽  
Thin Plates ◽  
Influence Functions ◽  
Algebraic Equations ◽  
Elastic Plates ◽  
The Real ◽  
Linear Algebraic Equations ◽  
The Moment

A numerical method for the linear analysis of thin plates of arbitrary plan form and subjected to arbitrary loading and boundary conditions is presented in this paper. This method is an extension of the Wu-Altiero method [1] where use has been made of the force influence function for an infinite plate, whereas the work contained in this paper is based on the use of the moment influence function of an infinite plate. The technique basically involves embedding the real plate into a fictitious infinite plate for which the moment influence function is known. N points are prescribed at the plate boundary at which the boundary conditions for the original problem are collocated by means of 2N fictitious moments placed around contours outside the domain of the real plate. A system of 2N linear algebraic equations in the unknown moments is obtained. The solution of the system yields the unknown moments. These may in turn be used to compute deflection, moments or shear at any point in the thin plate. Finally, the method is extended to include influence functions of both concentrated forces and concentrated moments. This is obtained by applying concentrated moments and forces simultaneously on the contours located outside the domain of the plate.

scholarly journals Robust methods for outlier detection and regression for SHM applications

2015 ◽  
Vol 2 (1/2) ◽  
pp. 3 ◽  
Author(s):  
Nikolaos Dervilis ◽  
Ifigeneia Antoniadou ◽  
Robert J. Barthorpe ◽  
Elizabeth J. Cross ◽  
Keith Worden
Keyword(s):  
Outlier Detection ◽  
Robust Methods

Outlier Detection for Compositional Data Using Robust Methods

2008 ◽  
Vol 40 (3) ◽  
pp. 233-248 ◽  
Author(s):  
Peter Filzmoser ◽  
Karel Hron
Keyword(s):  
Outlier Detection ◽  
Compositional Data ◽  
Robust Methods

scholarly journals Application of median-equation approach for outlier detection in geodetic networks

2013 ◽  
Vol 19 (4) ◽  
pp. 548-557 ◽  
Author(s):  
Serif Hekimoglu ◽  
Bahattin Erdogan
Keyword(s):  
Outlier Detection ◽  
A Priori ◽  
Breakdown Point ◽  
Data Sets ◽  
Robust Methods ◽  
Robust Method ◽  
High Breakdown Point ◽  
Point Estimator ◽  
Huber Method ◽  
The One

In geodetic measurements some outliers may occur sometimes in data sets, depending on different reasons. There are two main approaches to detect outliers as Tests for outliers (Baarda's and Pope's Tests) and robust methods (Danish method, Huber method etc.). These methods use the Least Squares Estimation (LSE). The outliers affect the LSE results, especially it smears the effects of the outliers on the good observations and sometimes wrong results may be obtained. To avoid these effects, a method that does not use LSE should be preferred. The median is a high breakdown point estimator and if it is applied for the outlier detection, reliable results can be obtained. In this study, a robust method which uses median with or as a treshould value on median residuals that are obtained from median equations is proposed. If the a priori variance of the observations is known, the reliability of the new approch is greater than the one in the case where the a priori variance is unknown.

The development of a linear influence function for an elastic half-space

1998 ◽  
Vol 33 (5) ◽  
pp. 357-362 ◽  
Author(s):  
C E Truman
Keyword(s):  
Influence Function ◽  
Piecewise Linear ◽  
Asymptotic Properties ◽  
Design Procedure ◽  
Piecewise Linear Function ◽  
Elastic Half Space ◽  
Influence Functions ◽  
Piecewise Constant ◽  
Linear Elements ◽  
Semianalytical Method

The determination of stresses induced in mechanical contacts arising in such components as gears, indenters and roller bearings is an important factor in the design procedure. In most cases the geometry of the contact problem is too complex to allow a full analytical solution. Some form of numerical method or semianalytical method must then be employed. The influence function method has so far been useful but limited due to the nature of the influence functions employed. Piecewise constant elements have been used where piecewise linear elements would give a more sophisticated solution. In this paper the influence functions for a hexagonal-based pyramid of pressure (the shape needed for a piecewise linear function) are derived and some of their asymptotic properties considered.

A Comparison of Outlier Detection Procedures and Robust Estimation Methods in GPS Positioning

2009 ◽  
Vol 62 (4) ◽  
pp. 699-709 ◽  
Author(s):  
Nathan L. Knight ◽  
Jinling Wang
Keyword(s):  
Outlier Detection ◽  
Robust Estimation ◽  
Estimation Methods ◽  
Robust Methods ◽  
Gps Measurements ◽  
Multiple Outliers ◽  
Satellite Systems ◽  
Gps Positioning ◽  
Outlier Test ◽  
Receiver Autonomous Integrity Monitoring

With more satellite systems becoming available there is currently a need for Receiver Autonomous Integrity Monitoring (RAIM) to exclude multiple outliers. While the single outlier test can be applied iteratively, in the field of statistics robust methods are preferred when multiple outliers exist. This study compares the outlier test and numerous robust methods with simulated GPS measurements to identify which methods have the greatest ability to correctly exclude outliers. It was found that no method could correctly exclude outliers 100% of the time. However, for a single outlier the outlier test achieved the highest rates of correct exclusion followed by the MM-estimator and the L1-norm. As the number of outliers increased MM-estimators and the L1-norm obtained the highest rates of normal exclusion, which were up to ten percent higher than the outlier test.

Sign in / Sign up

Export Citation Format

Share Document