Mahalanobis distance based on minimum regularized covariance determinant estimators for high dimensional data

Bulut, Hasan

doi:10.1080/03610926.2020.1719420

Cited by 12 publications

(7 citation statements)

References 14 publications

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“…In particular, for residuals, the Mahalanobis distance is considered sufficiently large if it exceeds the usual cut-off value χ 2 q,0.975 . However, for the distances of the explanatory variables, we use the cutoff proposed by [Bulut, 2020] because the distribution of the Mahalanobis distances calculated from the MRCD estimators is no longer chi-square. (4) shows the percentages of masking and swamping obtained.…”

Section: Masking and Swampingmentioning

confidence: 99%

“…To solve this inconvenience we make use of the proposal [Bulut, 2020] to determine a cut-off point that allows us to identify the observations with which we must calculate the reweighted version of the location vector and the scatter matrix of the observations z i . In particular, our reweighted estimators are the location vector and the scatter matrix of the observations z i that meet the following condition:…”

Section: Reweighted Minimum Regularized Covariance Estimator Regressi...mentioning

confidence: 99%

“…For the distances of the residuals, we use the usual cut-off value χ 2 q,0.975 1 . However, for the distances of the explanatory variables, we use the cut-off proposed by[Bulut, 2020] because the distribution of the Mahalanobis distances calculated from the MRCD estimators is no longer chisquare. We compare different methodologies (RMLC (Tukey), MRCDR, RMRCDR, RSPCR, RPCR) and as can be seen, similar results are obtained:…”

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confidence: 99%

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Robust multivariate regression for high-dimensional data

Santana,

González

2024

Preprint

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Multivariate multiple linear regression is a widely used statistical technique for modelling relationships between some response variables and several predictor variables. Traditional likelihood-based methods can produce very misleading results in the presence of outliers. In this work, we propose two robust multivariate regression methods designed to handle high-dimensional data: one based on the minimum regularized covariance determinant estimator, a robust estimator of location and scatter for high-dimensional data; and another based on dimensionality reduction using robust sparse principal component analysis. Through a study simulation, we evaluate the robustness and efficiency of the estimators obtained, the ability of the methodologies to correctly classify observations in contaminated datasets, and the computational cost. A real data application illustrates the use of the proposed methodologies.

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Section: Masking and Swampingmentioning

confidence: 99%

Section: Reweighted Minimum Regularized Covariance Estimator Regressi...mentioning

confidence: 99%

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confidence: 99%

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Robust multivariate regression for high-dimensional data

Santana,

González

2024

Preprint

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“…The appropriate method to use in the detection of outliers is the robust version of the Mahalanobis distance. Generally, the Minimum Covariance Determinant (MCD) estimators are used for this aim [18]. The MCD estimator proposed by Hubert et al [19], works by first finding the subset of observations that minimizes the determinant of the sample covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

Threshold Effects on Outlier Detection: A Comparative Study of MCD and MRCD Estimators in Multivariate Data Analysis

Yusuf,

Zachary

2023

AJPAS

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Aims: The aim of this study is to investigate the impact of thresholds on the detection of outliers by comparing the performance of two estimators, namely the minimum covariance determinant (MCD) and minimum regularized covariance determinant (MRCD), at different sample sizes. The study uses simulated data generated from the standard normal distribution to assess how varying thresholds affect the ability of these estimators to detect outliers. Study Design: This study employs a quantitative research design. It involves the generation of simulated data, the application of the MCD and MRCD estimators for outlier detection, and the systematic manipulation of thresholds and sample size as independent variables. Place and Duration: The study is conducted using computational tools and did not require a physical location. Methodology: Simulated data is generated from the standard normal distribution to create a controlled environment for outlier detection experiments. The MCD and MRCD estimators are applied to the simulated data to detect outliers. These estimators are sensitive to deviations from the norm in the data. Different thresholds are systematically applied to the data, and the performance of the estimators is assessed at each threshold level. Thresholds may vary in their extremeness. The study investigates the impact of different sample sizes on outlier detection. This involves using datasets with varying numbers of observations. The r programming language and associated packages are used as the statistical tool for data generation, analysis, and visualization. Results: The study's findings indicate that the choice of thresholds in data analysis significantly affects the performance of the MCD and MRCD estimators in outlier detection. If the thresholds used for both estimators are the same, their performance is similar. However, differences emerge when thresholds differ from each other. Higher thresholds are shown to identify less extreme outliers, while lower thresholds are effective at identifying more extreme outliers. These results provide insights into the behavior of these estimators in outlier detection scenarios, shedding light on their sensitivity to threshold choices and sample size.Conclusion: Our study has shed light on the critical interdependencies among threshold choices, sample sizes, and the performance of the minimum covariance determinant (MCD) and minimum regularized covariance determinant (MRCD) estimators in the context of outlier detection. By conducting a systematic exploration in a controlled environment with simulated data, we have gleaned valuable insights that can inform both researchers and practitioners in the field of organizational science research.

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“…The MCD estimator, used in the simulation study by Arslan (2012), cannot be applied to the case of high-dimensional data such as the simulation study in this paper. The MRCD estimator modifies the MCD estimator for high-dimensional data (Bulut, 2020). This estimator aims to regularize the covariance based on the subset that makes overall determinant the smallest (Boudt et al, 2019).…”

Section: A Introductionmentioning

confidence: 99%

Performance of LAD-LASSO and WLAD-LASSO on High Dimensional Regression in Handling Data Containing Outliers

Cahya

Sartono

Indahwati

et al. 2022

JTAM

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In several research areas, it is common to have a dataset with more explanatory variables than the number of observations, called high-dimensional data. This condition can lead to multicollinearity problem. The least absolute shrinkage and selection operator (LASSO) solves the problem by shrinking the estimated coefficient to zero so that it can simultaneously carry on the variable selection and the parameter estimation. But LASSO performs poorly when the data contains some outliers in the response or explanatory variables. Robust methods have addressed this problem based on the least-absolute-deviation approach, such as LAD-LASSO and WLAD-LASSO. This current research aims to evaluate the performance of the LAD-LASSO and WLAD-LASSO methods on high-dimensional and low-dimensional data containing outliers. To evaluate the performance of these methods, the simulation study was conducted. The simulation study used three scenarios (without outliers, outliers on the response variable (5%, 10%, 15%), outliers both on the response and explanatory variables (5%, 10%, 15%)). We also used the Minimum Regularized Covariance Determinant (MRCD) estimator in calculating the weights on the WLAD-LASSO. The best method from this simulation then will be applied to sembung leaf extract data to identify antioxidant marker compounds in sembung leaf extract. The simulation results show that LAD-LASSO tends to be very tight in selecting, while LASSO tends to be too loose. Meanwhile, WLAD-LASSO is in the middle of those two techniques and performs the best in identifying the important variables correctly. Even the existence of weights cause WLAD-LASSO more robust against the presence of outliers in the response and explanatory variables compared to LAD-LASSO. Furthermore, performance of these methods on high-dimensional data decrease compared to low-dimensional data. The performance of these methods also tends to decrease when the rate of outlier increases. The WLAD-LASSO was then implemented in actual data to find the compound of antioxidant markers in the sembung leaf extract. The compounds/formulas obtained are Umbelliferone, 12-Hydroxyjasmonic Acid, C22H14N8O2, and Acetyleugenol (with a prediction error is 0.133050). These compounds/formulas can be developed as natural antioxidants and have the potential to be developed as medicinal ingredients.

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Mahalanobis distance based on minimum regularized covariance determinant estimators for high dimensional data

Cited by 12 publications

References 14 publications

Robust multivariate regression for high-dimensional data

Robust multivariate regression for high-dimensional data

Threshold Effects on Outlier Detection: A Comparative Study of MCD and MRCD Estimators in Multivariate Data Analysis

Performance of LAD-LASSO and WLAD-LASSO on High Dimensional Regression in Handling Data Containing Outliers

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