Hazlina Ali

Robust linear discriminant models to solve financial crisis in banking sectors

Linear discriminant analysis (LDA) is a widely-used technique in patterns classification via an equation which will minimize the probability of misclassifying cases into their respective categories. However, the performance of classical estimators in LDA highly depends on the assumptions of normality and homoscedasticity. Several robust estimators in LDA such as Minimum Covariance Determinant (MCD), S-estimators and Minimum Volume Ellipsoid (MVE) are addressed by many authors to alleviate the problem of non-robustness of the classical estimates. In this paper, we investigate on the financial crisis of the Malaysian banking institutions using robust LDA and classical LDA methods. Our objective is to distinguish the “distress” and “non-distress” banks in Malaysia by using the LDA models. Hit ratio is used to validate the accuracy predictive of LDA models. The performance of LDA is evaluated by estimating the misclassification rate via apparent error rate. The results and comparisons show that the robust est...

Winsorization on linear discriminant analysis

Linear discriminant analysis (LDA) is a widely used multivariate technique for pattern classification. LDA creates an equation which can minimize the possibility of misclassifying observations into their corresponding populations. The main objective of LDA is to classify multivariate data into different populations on the basis of a training sample with known group memberships. Under ideal conditions that is when the distribution is normal and variances are equal (homoscedasticity), LDA performs optimally. Nevertheless, the classical estimates, sample mean and sample covariance, are highly affected when the ideal conditions are violated. To alleviate these problems, a new robust LDA model using winsorized approach to estimate the location measure to replace the sample mean was introduced in this study. Meanwhile, for the robust covariance, the product of Spearman’s rho and the rescaled median absolute deviation was used as the substitute for the classical covariance. The optimality of the proposed model i...

A computationally efficient of robust mahalanobis distance based on MVV estimator

MCD is a well-known multivariate robust estimator. However, the computation of the estimator is not simple especially for large sample size due to the complexity of the objective function i.e. minimizing covariance determinant. Recently, an alternative objective function which is simpler and faster was introduced. The objective function is to minimize vector variance, which consequently will generate the estimator known as minimum vector variance (MVV). In this paper, a simulation study was conducted to compare the computational efficiency of the two estimators with regards to the number of operations in the computation of objective function and also iterations of the algorithm to convergence. The result showed that the computational efficiency of MVV is higher than MCD for small or large data set.

The efficiency of reweighted minimum vector variance

Minimum vector variance (MVV) is a new robust estimator which possesses the good properties as in minimum covariance determinant (MCD), but with better computational efficiency. However, the highly robust affine equivariant estimators with the best breakdown point commonly have to compensate with low statistical efficiency. Hence, to increase the efficiency while retaining the highest breakdown point, we proceed to improve the MVV estimators in the context of statistical efficiency via reweighted version (RMVV). Interestingly, the reweighted scheme was able to maintain the breakdown point of 0.5 and attained higher efficiency at the normal distribution.

Robust Hotelling Control Chart with Consistent Minimum Vector Variance

Recently, an alternative robust control chart based on a new robust estimator known as minimum vector variance (MVV) estimator, , was introduced in Phase II. was able to detect out-of-control signal and simultaneously control false alarm rate even as the dimension increased. However, the estimated UCLs of are large as compared to the traditional chart. In this study, we improved the MVV estimators in terms of consistency and bias. The result showed great improvement in the control limit values while maintaining its good performance in terms of false alarm and probability of detection.

Robust linear discriminant analysis with distance based estimators

Linear discriminant analysis (LDA) is one of the supervised classification techniques concerning relationship between a categorical variable and a set of continuous variables. The main objective of LDA is to create a function to distinguish between populations and allocating future observations to previously defined populations. Under the assumptions of normality and homoscedasticity, the LDA yields optimal linear discriminant rule (LDR) between two or more groups. However, the optimality of LDA highly relies on the sample mean and pooled sample covariance matrix which are known to be sensitive to outliers. To alleviate these conflicts, a new robust LDA using distance based estimators known as minimum variance vector (MVV) has been proposed in this study. The MVV estimators were used to substitute the classical sample mean and classical sample covariance to form a robust linear discriminant rule (RLDR). Simulation and real data study were conducted to examine on the performance of the proposed RLDR measur...

An EWMA chart for sample range of Weibull data using weighted variance method

This article proposes new EWMA chart in observing process standard deviation or dispersion with sample range of Weibull data using weighted variance method (WV). This control chart, called Weighted Variance EWMA sample range WV-EWMASR chart hereafter. The proposed WV-EWMASR chart compared with standard EWMASR of [7], skewness correction R chart (SC-R) suggested by[3]and Weighted Variance R chart (WV-R) proposed by [2], in the case of Type I and Type II errors when the data generated from Weibull distribution. Optimal parameters λ and k of the proposed WV-EWMASR and standard EWMASR are obtained via simulation using SAS program 9.4. The proposed WV-EWMASR control chart reduces to the standard EWMASR control chart of [7] when the process follow symmetric distribution. The proposed WV-EWMASR control chart has less Type I error than the standard EWMASR, SC-R and WV-R control charts, for Weibull distribution data. In case of Type II error, the proposed WV-EWMASR control chart is closer to EWMA chart with the ex...

Robust parameter estimation method for bilinear model

This paper proposed the method of parameter estimation for bilinear model, especially on BL(1,0,1,1) model without and with the presence of additive outlier (AO). In this study, the estimated parameters for BL(1,0,1,1) model are using nonlinear least squares (LS) method and also through robust approaches. The LS method employs the Newton-Raphson (NR) iterative procedure in estimating the parameters of bilinear model, but, using LS in estimating the parameters can be affected with the occurrence of outliers. As a solution, this study proposed robust approaches in dealing with the problem of outliers specifically on AO in BL(1,0,1,1) model. In robust estimation method, for improvement, we proposed to modify the NR procedure with robust scale estimators. We introduced two robust scale estimators namely median absolute deviation (MADn) and Tn in linear autoregressive model, AR(1) that be adequate and suitable for bilinear BL(1,0,1,1) model. We used the estimated parameter value in AR(1) model as an initial va...

ENHANCING MINIMUM VECTOR VARIANCE ESTIMATORS USING REWEIGHTED SCHEME

Minimum vector variance (MVV) is one of the latest contributions in the study of multivariate robust estimators.MVV estimators possess three important properties of a good robust estimator, namely, high breakdown point, affine equivariance and computational efficiency.However, highly robust affine equivariant estimators with the best breakdown point commonly have to compensate with low statistical efficiency.In order to cater this drawback, a reweighted minimum vector variance (RMVV) which is capable of increasing the efficiency while retaining the highest breakdown point is proposed in this paper.A simulation study was conducted to investigate the asymptotic relative efficiency and finite-sample behavior of the estimators for several types of distributions. The numerical results revealed that the reweighed scheme is able to attain higher efficiency compared to MVV estimators.

The Application of Consistent Minimum Vector Variance (MVV) Estimators on Hotelling T2 Control Chart

Traditional Hotelling T 2 control chart is sensitive to the masking and swamping effect. Recently, an alternative robust control chart based on a new robust estimator known as minimum vector variance (MVV) estimator, denoted as T MVV 2 , was introduced in Phase II data. In general, T MVV 2 was able to detect out-of-control signal and simultaneously control false alarm rate even as the dimension increased. However, the estimated upper control limits (UCL) of T MVV 2 were large compared to the traditional chart. To tackle this problem, we multiplied the constant correction factors to obtain consistency at multivariate normal data and guarantee asymptotic unbiased of MVV estimators. The improved MVV estimators were applied in Hotelling T 2 chart by using real data from aircraft industry. The result showed great improvement in the control limit values while maintaining its good performance in terms of probability of detection.