Alternative Estimator for Multivariate Location and Scatter Matrix in the Presence of Outlier
Journal Title: Annals. Computer Science Series - Year 2018, Vol 16, Issue 2
Abstract
It is generally known that in estimating location and scatter matrix of multivariate data when outliers are presents, the method of classical is not robust. The Maximum Likelihood Estimator (MLE) is always very sensitive to some deviations from the assumptions made on the data, especially, presence of outliers. To get over the above stated problem, many alternative estimators that are robust have been proposed in the last decades. Some of these estimators include the Minimum Covariance Determinant (MCD), the Minimum Volume Ellipsoid (MVE), S-Estimators, M-Estimators and Minimum Regularized Covariance Determinant (MRCD) among others. All the methods converged on tackling the problem of robust estimation by finding a sufficiently large subset of the data. In this paper, a robust method of estimating multivariate location and scatter matrix in the presence of outliers is proposed. The proposed estimator is obtained using the best units (samples) from the available data set that satisfied a set of three optimality criteria (CA,CH,CG).The performance of the proposed robust method was compared with two of the existing robust methods (MCD and MVE) and the classical method with their application in Principal component analysis data simulation. The measure of performance used was the Mean Square Errors (MSE) of the characteristic roots (eigen-values) of the variance-covariance matrix. Generally, the proposed alternative method is better than other robust methods and classical method, when the level of magnitude of outliers is small and also performed considerably well with MCD and MVE when the level of magnitude is high at all percentages of outliers.
Authors and Affiliations
Oluwafemi Samuel OBAFEMI, Gafar Matanmi OYEYEMI
Keywords
Related Articles
- EP ID EP550066
- DOI -
- Views 103
- Downloads 0
How many interchanges does the selection sort make for iid geometric(p) input?
The note derives an expression for the number of interchanges made by selection sort when the sorting elements are iid variates from geometric distribution. Empirical results reveal we can work with a simpler model compa...
Constructing and Exploring Triangles with GeoGebra
We look at a new approach to mathematical constructions. Using GeoGebra, we first do dynamic analysis and exploration. Again with GeoGebra, we then do a strict compass and straightedge constructions. Finally and yet agai...
Information Access in the Digital Era
With a fast evolution, a considerable number of applications and global accessibility, the internet is used, nowadays, to gather information from every field of interest, for business dealings, for establishing social re...
Performance Evaluation of Implementation Languages on Cognitive Complexity of Dijkstra Algorithm
Maintainability is a key factor in measuring the quality of developed software and it becomes important due to dynamism of software. Partially, maintainability is a function of source code understandability on the part o...
Performance Evaluation of PSO, PSOCA and MPSOCA for Solving University Timetabling Problem
In this paper, performance evaluation of Particle Swarm Optimization algorithm (PSO), Particle Swarm Optimization based Cultural Algorithm (PSOCA) and Modified Particle Swarm Optimization based Cultural Algorithm (MPSOCA...