Sharipah Soaad Syed Yahaya

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...

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.

Sensitivity analysis of Welch’s t-test

Welch t-test is the parametric test for comparing means between two independent groups without assuming equal population variances. This statistic is robust for testing the mean equality when homogeneity assumption is not satisfied, but Welch test is not always robust. When multiple problems such as the distribution is non-normal, variance is heterogeneous and unequal size of groups occur simultaneously, the Type I error will inflate. In this study, various conditions such as sample sizes, type of distributions and unequal group variances were manipulated to investigate on the non robust conditions of Welch test. The Type I error rates and power of the test for different design specifications were obtained and compared. The results indicated that this test did not perform well under non-normal distributions especially when group sizes and unequal group variances are inversely associated or negatively paired. The estimated Type I error inflated as the power of the test improved.

Performance of the modified Wilcoxon signed rank test

Nonparametric methods require only few assumptions to be made about the format of the data, and they may therefore be preferable when the assumptions required for parametric methods are not valid. The Wilcoxon signed rank test applies to matched pairs studies. For two tail test, it tests the null hypothesis that there is no systematic difference within pairs against alternatives that assert a systematic difference. The test is based on the Wilcoxon signed rank statistic W, which is the smaller of the two ranks sums. The steps to compute W consider the positive and negative differences and omit all the zero differences. In this study, we modify the Wilcoxon signed rank test using the indicator function of positive, zero and negative differences to compute the Wilcoxon statistic, W. The empirical Type I error rates of the modified statistical test was measured via Monte Carlo simulation. These rates were obtained under different distributional shapes, sample sizes, and number of replications. The modified Wilcoxon signed rank test was found to be robust under symmetric distributions even though the values are quite conservative. The finding also demonstrated that different number of replication does not influence the result because there is not much difference in the value of the Type I error rates obtained.Nonparametric methods require only few assumptions to be made about the format of the data, and they may therefore be preferable when the assumptions required for parametric methods are not valid. The Wilcoxon signed rank test applies to matched pairs studies. For two tail test, it tests the null hypothesis that there is no systematic difference within pairs against alternatives that assert a systematic difference. The test is based on the Wilcoxon signed rank statistic W, which is the smaller of the two ranks sums. The steps to compute W consider the positive and negative differences and omit all the zero differences. In this study, we modify the Wilcoxon signed rank test using the indicator function of positive, zero and negative differences to compute the Wilcoxon statistic, W. The empirical Type I error rates of the modified statistical test was measured via Monte Carlo simulation. These rates were obtained under different distributional shapes, sample sizes, and number of replications. The modified W...

Median based robust correlation coefficient

Real datasets usually include a fraction of outliers and other contaminations. The classical correlation coefficient is much affected by these outliers and often gives misleading results. The problem of computing the correlation estimate from bivariate data containing a portion of outliers has been deliberated in this study. The classical correlation uses non-robust mean and standard deviation as the location and scale estimator respectively. In this study, two robust correlation coefficients based on high breakdown point median estimator were examined. The performance of the classical correlation together with the robust correlation coefficient was measured and compared in terms of the correlation value, average bias and standard error for the clean and contaminated data. Simulation studies reveal that all correlation coefficients perform well for clean data. However, under contaminated data, the findings show that median based robust correlation coefficient gives better results as compared to the classical correlation coefficient.Real datasets usually include a fraction of outliers and other contaminations. The classical correlation coefficient is much affected by these outliers and often gives misleading results. The problem of computing the correlation estimate from bivariate data containing a portion of outliers has been deliberated in this study. The classical correlation uses non-robust mean and standard deviation as the location and scale estimator respectively. In this study, two robust correlation coefficients based on high breakdown point median estimator were examined. The performance of the classical correlation together with the robust correlation coefficient was measured and compared in terms of the correlation value, average bias and standard error for the clean and contaminated data. Simulation studies reveal that all correlation coefficients perform well for clean data. However, under contaminated data, the findings show that median based robust correlation coefficient gives better results as compared to the classi...

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...

New S control chart using skewness correction method for monitoring process dispersion of skewed distributions

Control chart is established as one of the most powerful tools in Statistical Process Control (SPC) and is widely used in industries. The conventional control charts rely on normality assumption, which is not always the case for industrial data. This paper proposes a new S control chart for monitoring process dispersion using skewness correction method for skewed distributions, named as SC-S control chart. Its performance in terms of false alarm rate is compared with various existing control charts for monitoring process dispersion, such as scaled weighted variance S chart (SWV-S); skewness correction R chart (SC-R); weighted variance R chart (WV-R); weighted variance S chart (WV-S); and standard S chart (STD-S). Comparison with exact S control chart with regards to the probability of out-of-control detections is also accomplished. The Weibull and gamma distributions adopted in this study are assessed along with the normal distribution. Simulation study shows that the proposed SC-S control chart provides ...

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...

The performance of robust correlation coefficient under contaminated bivariate data

Classical correlation coefficient is a powerful statistical analysis when measuring a relationship between the bivariate normal distribution when the assumptions are fulfill. However, this classical correlation coefficient performs poor in the presence of outlier. Thus, this study aims to propose new version of robust correlation coefficient based on MADn and Sn. The performance of this proposed robust correlation coefficient will be evaluated based on three indicators which were the value of the correlation coefficient, average bias and standard error. The proposed procedure is expected to produce MADn correlation coefficient and Sn correlation coefficient. Both coefficients are expected to perform better than classical correlation coefficient and resistance to the outlier.