BUKU ABSTRAK - Universiti Putra Malaysia

Diagnostic-robust Generalised Potentials for the Identification of Multiple High
Leverage Points
Assoc. Prof. Dr. Habshah Midi
Norazan Mohamed Ramli and A.H.M.R. Imon
Institute of Mathematical Research, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
+603-8946 6876; habshahmidi@gmail.com
Mutual Information for Mixture of Bivariate Normal Distributions based on
Robust Kernel Estimation
Assoc. Prof. Dr. Habshah Midi
Kourosh Dadkhah
Institute of Mathematical Research, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
+603-8946 6876; habshahmidi@gmail.com
247
Science, Technology & Engineering
Leverage values are being used in regression diagnostics as measures of influential observations in the
X-space. Detection of high leverage values is crucial due to their responsibility for misleading conclusion about
the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers etc.
Much work has been done on the identification of single high leverage points and it is generally believed that the
problem of detection of a single high leverage point has been largely resolved. But there is no general agreement
among the statisticians about the detection of multiple high leverage points. When a group of high leverage
points is present in a data set, mainly due to the masking and/or swamping effects the commonly used diagnostic
methods fail to identify them correctly. On the other hand, the robust alternative methods can identify the high
leverage points correctly but they have a tendency to identify too many low leverage points to be points of high
leverages which are not desired. In this paper an attempt has been made to make a compromise between these
two approaches. We propose an adaptive method where the suspect high leverage points are identified by robust
methods and then the low leverage points (if any) are put back into the estimation data set after diagnostic
checking. The usefulness of our newly proposed method for the detection of multiple high leverage points is
studied by some well-known data sets and Monte Carlo simulations.
Keywords: High leverage points, masking, group deletion, Robust Mahalanobis distance, minimum volume ellipsoid,
diagnostic-robust generalised potentials, Monte Carlo simulation
Mutual Information (MI) measures the degree of association between variables in nonlinear model as well
as linear models. It can also be used to measure the dependency between variables in mixture distribution. The
MI is estimated based on the estimated values of the joint density function and the marginal density functions of
X and Y. A variety of methods for the estimation of the density function have been recommended. In this study,
we only considered the kernel method to estimate the density function. However, the classical kernel density
estimator is not reliable when dealing with mixture density functions which prone to create two distant groups in
the data. In this situation, a robust kernel density estimator is proposed to acquire a more efficient MI estimate in
mixture distribution. The performance of the robust MI is investigated extensively by Monte Carlo simulations.
The results of the study offer substantial improvement over the existing techniques.
Keywords: Mutual information, kernel density, minimum volume ellipsoid, minimum covariance determinant, outliers,
mixture distribution, robust statistics