Trimmed Square Research Articles

Comparative Study in Controlling Outliers and Multicollinearity Using Robust Performance Jackknife Ridge Regression Estimator Based on Generalized-M and Least Trimmed Square Estimator

Regression analysis is one of the statistical methods used to determine the causal relationship between one or more explanatory variables to the affected variable. The problem that often occurs in regression analysis is that there are multicollonity and outliers. To deal with such problems can be solved using ridge regression analysis and robust regression. Ridge regression can solve the problem of multicollinearas by assigning a constant k to the matrix Z′Z. But in this method the resulting bias value is still high, so to overcome this problem, the jackknife ridge regression method is used. Meanwhile, to overcome outliers in the data using robust regression methods which have several estimation methods, two of which are the Generalized-M (GM) estimator and the Least Trimmed Square (LTS) estimator. The aim of the study is to solve the problem of multicollinearity and outliers simultaneously using robust jackknife ridge regression method with GM estimators and LTS estimators. The results showed that the robust ridge jackknife regression method with LTS estimator can control multicollinearity and outliers simultaneously better based on MSE, AIC and BIC values compared to the robust ridge jackknife regression method with GM estimators. This is indicated by the value MSE = -6.60371, AIC = 75.823 and BIC = 81.642 on LTS estimators that are of lower value than GM estimators.

Estimasi Parameter Regresi Ridge Robust pada Data Profil Kesehatan Sulawesi Selatan

ABSTRACT Multicollinearity is one of the assumption violations in regression analysis. The existence of multicollinearity causes the standard error to increase. Ridge regression is one of the regression analysis approaches that can overcome this problem. Besides multicollinearity, another problem that often occurs is outliers. The existence of outliers causes the data not to be normally distributed. Ridge Robust Least Trimmed Square Regression is a method that can be used to overcome multicollinearity and outlier problems in the data simultaneously in the regression analysis model. The purpose of this study was to obtain the estimation results of the least trimmed square ridge robust regression model on the Health Profile data of South Sulawesi in 2017. From the results and discussion it was found that the least trimmed square ridge robust regression method has an Rsquare value or ?2 which is 88% and an MSE value 1.96, thus indicating that the ridge robust least trimmed square model fits better in dealing with data containing multicollinearity and outliers. Keywords: Robust Ridge Regression, Least Trimmed Square, Multicollinearity, Outlier, Infant Mortality Rate.

Perbandingan Analisis Komponen Utama Robust Minimum Covarian Determinant dengan Least Trimmed Square pada Data Produk Domestik Regional Bruto

Regression analysis is a method to examine the relationship between variables and determine their influence. However, the problem of multicollinearity often arises in linear regression analysis and can cause interpretation problems. To handle multicollinearity, Principal Component Analysis (PCA) is used. However, this method has a weakness when the data contains outliers. Therefore, it was developed into robust PCA using the Minimum Covariance Determinant (MCD) method and the Least Trimmed Square (LTS) estimation method. This study uses Gross Regional Domestic Product data in Indonesia in 2020, which has problems with multicollinearity and outliers. This data is modeled using two robust PCA methods, namely MCD and LTS. The robust PCA model with MCD has an adjusted value of 87.87% and an MSE value of 0.0700. However, in the robust PCA regression model with LTS, the adjusted value is 98.93% and the MSE value is 0.0325. Thus, the effective method in handling multicollinearity and outliers is the LTS method because it shows better results.

Florbetapir PET Uptake in White Matter in Aging and Alzheimer’s Disease

AbstractBackgroundAmyloid PET tracers, typically used to track cerebral amyloid changes in Alzheimer’s Disease (AD) patients, have been recently suggested to measure cerebral white matter (WM) integrity due to structural similarity between myelin and amyloid. We previously reported significant associations of amyloid neuroimaging marker, Pittsburgh Compound B (PiB) PET, with WM hyperintensities as quantified by MRI and FLAIR data, in AD patients (Su et al. 2018, HAI). The goal of this study was to explore the association between Florbetapir (FBP) PET and WM integrity.MethodOur study population consisted of 673 participants from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) sorted into the following groups of clinical severity: (1) Normal Controls (NC) participants who are amyloid negative and cognitively normal (CDR = 0) (A‐CDR‐); (2) Preclinical (Pre) who are cognitively normal (CDR = 0) and amyloid positive (A+CDR0); (3) Symptomatic AD who are both CDR and amyloid positive (A+CDR+); and (4) Suspected Other Dementia group consisting of cognitively impaired but amyloid negative participants. We analyzed baseline biomarkers as function of stage of AD and age, comparing groups using ANOVA and Scheffe’s Post Hoc Analysis, and linear regression, respectively. Associations between white matter and amyloid FBP uptake were quantified using Pearson correlation with Least Trimmed Square (LTS) regression. Lastly, rate of change of amyloid and white matter uptake of FBP PET were quantified to assess longitudinal biomarker changes using a one sample t‐test.ResultCross‐sectionally, baseline FBP uptake in white matter significantly declines with age (p = 0.027) and advancing disease stage with significant differences found between the Preclinical and Symptomatic AD group (p<2.2E‐06); and NC and Symptomatic AD group (p<0.003). Significant associations were also observed between baseline FBP uptake in white matter and amyloid (p<0.001).Longitudinally, rate of change of FBP uptake in white matter progressively declined with advancing disease stage while rate of change of FBP uptake in amyloid increased and plateaued in the Symptomatic group of patients.ConclusionAltogether, our results show declining FBP uptake by white matter, both cross‐sectionally and longitudinally, through the stages of AD and with age. Our results could have methodological implications on the quantification of amyloid burden using WM as a reference region.

Review of Some Robust Estimators in Multiple Linear Regressions in the Presence of Outlier(s)

Linear regression has been one of the most important statistical data analysis tools. Multiple regression is a type of regression where the dependent variable shows a linear relationship with two or more independent variables. OLS estimate is extremely sensitive to unusual observations (outliers), with low breakdown point and low efficiency. This paper reviews and compares some of the existing robust methods (Least Absolute Deviation, Huber M-Estimator, Bisquare M-Estimator, MM Estimator, Least Median Square, Least Trimmed Square, S-Estimator); a simulation method is used to compare the selected existing methods. It was concluded based on the results that for y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.3 is MM; for x direction outlier, the best estimator in term breakdown point of at most 0.4 is S; for x, y direction outlier, the best estimator in terms of high efficiency and breakdown point of at most 0.2 is MM.

Analisis Regresi Robust Estimasi Least Trimmed Square dan Estimasi Maximum Likelihood pada Pemodelan IPM di Pulau Sulawesi

Sulawesi Island is one of the islands in Indonesia with the second lowest HDI after Papua in 2011-2018, so it is necessary to study more deeply the factors that affect the HDI on Sulawesi Island. One of the methods in modeling is the robust regression method that can be used even though there are outliers in the data. This study aimed to determine the factors that affect HDI in Sulawesi Island using a robust regression model of Least Trimmed Square (LTS) estimation and Maximum Likelihood (M) estimation and to find out the best method for modeling HDI in Sulawesi Island. The robust regression of the LTS estimate has a reasonably high breakdown point value compared to other estimates, while the M-estimate has a high efficiency. The results showed that the factors that affect HDI on the island of Sulawesi are Life Expectancy (UHH), Expected Years of Schooling (HLS), Average Years of Schooling (RLS), and Real Expenditures per capita (PPP). The best model in HDI modeling in Sulawesi Island is a robust regression model with LTS estimation where the standard error is 0.1513, and the R-Square is 99.78%. A very high R-Square value indicates that the ability of the UHH, HLS, RLS, and PPP variables to explain HDI is very good.

LPRNet: A Novel Approach for Novelty Detection in Networking Packets

Novelty Detection is a task of recognition of abnormal data points within a given system. Recently, this task has been performed using Deep Learning Autoencoders, but they face several drawbacks which include the problem of identity mapping, adversarial perturbations and optimization algorithms. In this paper, we have proposed a novel approach LPRNet, a Denoising Autoencoder which uses algorithms such as Least Trimmed Square, Projected Gradient Descent and Robust Principal Component Analysis, to solve the above-mentioned problems. LRPNet is then trained and tested on NSL-KDD dataset, and experiments have been performed using Accuracy as performance metric for comparing the existing models with the proposed model. The results show that LRPNet has the maximum accuracy of 95.9% and performed better than all the previous state-of-the-art algorithms.

Response Surface Regression with LTS and MM-Estimator to Overcome Outliers on Red Roselle Flowers

The surface response method is similar to the regression analysis method which uses procedures or ways of estimating the response function regression model based on the Ordinary Least Square (OLS) method. Unfortunately, using the quadratic method has no drawbacks because it is easily sensitive to assumption deviations due to outlier cases. One of the solutions to the outlier problem is using robust regression. The method of parameters in the regression is very diverse, but the methods used in this study are the Least Trimmed Square (LTS) and MM-estimator methods because both methods have a high breakdown point of nearly 50%. The variables studied were the response variable consisting of red roselle plant height (Y1) and red roselle flower weight (Y2). While the independent variables were soil moisture factor (X1) and NPK fertilizer application factor (X2). The purpose of this study is to estimate the response surface regression parameters. using the LTS and MM-estimator methods on data that contains outliers. The resulting model in data analysis shows the same result that the best model is using the LTS estimation method. The modeling result of plant height obtained an R-Square value of 98,27% with an error is 1,243. Meanwhile, for the red rosella plant flower weight model, the R-Square value was 97,31% with an error is 0.6632.

Analysis of Efficiency of Least Trimmed Square and Least Median Square Methods in The Estimation of Robust Regression Parameters

<span lang="EN">Robust regression is a regression method used when the remainder's distribution is not reasonable, or there is an outreach to observational data that affects the model. One method for estimating regression parameters is the Least Squares Method (MKT). The method is easily affected by the presence of outliers. Therefore we need an alternative method that is robust to the presence of outliers, namely robust regression. Methods for estimating robust regression parameters include Least Trimmed Square (LTS) and Least Median Square (LMS). These methods are estimators with high breakdown points for outlier observational data and have more efficient algorithms than other estimation methods. This study aims to compare the regression models formed from the LTS and LMS methods, determine the efficiency of the model formed, and determine the factors that influence the production of community oil palm in Langkat District in 2018. The results showed that in testing, the estimated model of the regression parameters showed the same results. Compared to the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018</span>

Analisis Regresi Komponen Utama Robust dengan Metode Minimum Covariance Determinant – Least Trimmed Square (MCD-LTS)

Principal Component Regression (PCR) is a method used to overcome multicollinearity problems by reducing the dimensions of independent variables to obtain new simpler variables without losing most of the information contained in the variables. If the data analyzed contain outliers, a robust method on PCR is required. In this paper we use a robust method which is a combination of Robust Principal Component Analysis using the Minimum Covariance Determinant (MCD) method and Robust Regression Analysis using Least Trimmed Square (LTS) method. The purpose of this study is to examine the robust PCR analysis using the MCD-LTS method and to know the robustness of the method by looking at its sensitivity to outliers. For this purpose we compared the MCD-LTS PCR to the classic PCR based on the bias and Mean Square Error (MSE) values on several different sample sizes and percentages of outliers. The results of this study indicate that robust PCR using MCD-LTS is effective and efficient in overcoming the problem of multicollinearity and outliers in regression analysis.

An Evaluation of the Impact of Multicollinearity on the Performance of Various Robust Regression Methods

Objectives: To examine the performance of several regression methods comprising of Ordinary Least Square (OLS), and certain robust methods including; M-regression, Least Median of Squared (LMS), Least Trimmed Square (LTS), MMestimation and S-estimation, under fluctuating levels of collinearity, using the criterion, Total Absolute Deviation (TAB) and Total Mean Square Error (TMSE) with some graphical tools. Methods/Statistical Analysis: Robust Regression methods insure good performance even in case the fundamental assumption of normality is not satisfied. The presence of multicollinearity affects the results of robust regression methods and marks them unsatisfactory. A quantitative evaluation of these techniques is provided by using the criterion, TAB and TMSE. Results are summarised by using box plot of absolute bias, along with the graphs of TAB, and TMSE. Findings: The results show that for minor levels of collinearity the effect is low and similar, but at greater levels of collinearity the effect is high and performance wise all the methods give quite incompatible results. It is also illustrated that greater magnitude of collinearity along with higher percentages of outliers ranks the underlying methods quite differently, resulting in MM-estimation method to be the most unpleasant. Conclusion: While applying any statistical method it is necessary to consider all the assumption underlying that method as well as every aspect of our data to avoid misleading results. It is illustrated that MM-estimation method although a best candidate for higher percentages of outliers alone, become the most unpleasant, by a simultaneous interruption of high level of collinearity, hence robust ridge techniques need to be adopted. Keywords: Multicollinearity, Ordinary Least Squares, Outliers, Robust Regression Methods

Reexamination of Estimating Beta Coefficient as a Risk Measure in CAPM

This research examines the alternative ways of estimating the coefficient of non-diversifiable risk, namely beta coefficient, in Capital Asset Pricing Model (CAPM) introduced by Sharpe (1964) that is an essential element of assessing the value of diverse assets. The non-parametric methods used in this research are the robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MM-estimator). The Jackknife, the resampling technique, is also employed to validate the results. According to finance literature and common practices, these coecients have often been estimated using Ordinary Least Square (LS) regression method and monthly return data set. The empirical results of this research pointed out that the robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MM-estimator) performed much better than Ordinary Least Square (LS) in terms of eciency for large-cap stocks trading actively in the United States markets. Interestingly, the empirical results also showed that daily return data would give more accurate estimation than monthly return data in both Ordinary Least Square (LS) and robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MM-estimator) regressions.

Analysis Method of Dam Safety Monitoring Data Based on the Least Trimmed Square Estimation

The water engineering safety monitoring data inevitably existed outliers, but the most widely used least squares method (LS) had no ability to remove the outliers. And the LS was more easily disturbed by the outliers to mistake the actual regression curves. Aiming at the defects of LS, the least trimmed squares (LTS) was introduced, based on the least minimizing residual sum of squares, to construct the water engineering safety monitoring model. According to and analyzing monitoring data of actual project, the optimal data groups were obtained by removing the outliers. And then the most practical fitting curve was obtained by getting the regression coefficient of the optimal data groups. Compared with the least square method, the LTS results were more reasonable and robust. Meanwhile, the prediction accuracy of the data was significantly improved. Therefore, the LTS was great prospect for the water engineering safety monitoring data analysis.

Wavelet Neural Networks for DNA Sequence Classification Using the Genetic Algorithms and the Least Trimmed Square

This paper presents a structure of the Wavelet Neural Networks used to classify the DNA sequences. The satisfying performance of the Wavelet Neural Networks (WNN) depends on an appropriate determination of the WNN structure optimization problem. In this paper we present a new method to solve this problem based on Genetic Algorithm (GA) and the Least Trimmed Square (LTS). The GA is used to solve the structure and the learning of the WNN and the LTS algorithm is applied to select the important wavelets. First, the scale of the WNN is managed by using the time-frequency locality of wavelet. Furthermore, this optimization problem can be solved efficiently by Genetic Algorithm as well as the LTS method to improve the robustness. The performance of the Wavelet Networks is investigated by detecting the simulating and the real signals in white noise. The main advantage of this method can guarantee the optimal structure of the WNN. The experimental results have indicated that the proposed method (WNN-GA) with the k-means algorithm is more precise than other methods. The proposed method has been able to optimize the wavelet neural network and classify the DNA sequences. Our goal is to construct a predictive approach that is highly accurate results. In fact, our approach allows avoiding the complex problem of form and structure in different groups of organisms. The experimental results are showed that the WNN-GA model outperformed the other models in terms of both the clustering results and the running time. In this study, we present our system which consists of three phases. The first one is the transformation, is composed of two sub steps; the binary codification of the DNA sequences and the Power Spectrum Signal Processing. The second step is the approximation; it is empowered by the use of the Multi Library Wavelet Neural Networks (MLWNN). Finally, the third one is the clustering of the DNA sequences, is realized by applying the algorithm of the k-means algorithm.

Least trimmed euclidean deviations for robust leverage in regression estimates

Usually, in the regression models, the data are contaminated with unusually observations (outliers). For that reason the last 30years have developed robust regression estimators. Among them some of the most famous are Least Trimmed Squares (LTS), MM, Penalized Trimmed Square (PTS) and others. Most of these methods, especially PTS, are based on initial leverage, concerning x outlying observations, of the data sample. However, often, multiple x-outliers pull the distance towards their value, causing leverage bias, and this is the masking problem.In this work we develop a new algorithm for robust leverage estimate based on Least Trimmed Euclidean Deviations (LTED). Extensive computational, Monte-Carlo simulations, with varying types of outliers and degrees of contamination, indicate that the LTED procedure identifies successfully the multiple outliers, and the resulting robust leverage improves significantly the PTS performance.

A Least Trimmed Square Regression Method for Second Level fMRI Effective Connectivity Analysis

We present a least trimmed square (LTS) robust regression method to combine different runs/subjects for second/high level effective connectivity analysis. The basic idea of this method is to treat the extreme nonlinear model variability as outliers if they exceed a certain threshold. A bootstrap method for the LTS estimation is employed to detect model outliers. We compared the LTS robust method with a non-robust method using simulated and real datasets. The difference between LTS and the non-robust method for second level effective connectivity analysis is significant, suggesting the conventional non-robust method is easily affected by the model variability from the first level analysis. In addition, after these outliers are detected and excluded for the high level analysis, the model coefficients of the second level are combined within the framework of a mixed model. The variance of the mixed model is estimated using the Newton-Raphson (NR) type Levenberg-Marquardt algorithm. Three sets of real data are adopted to compare conventional methods which do not include random effects in the analysis with a mixed model for second level effective connectivity analysis. The results show that the conventional method is significantly different from the mixed model when greater model variability exists, suggesting there is a strong random effect, and the mixed model should be employed for the second level effective connectivity analysis.

Data Truncation Bias, Loss Firms, and Accounting Anomalies

After performing a Least Trimmed Square procedure at 1%, Kraft, Leone, and Wasley (2006) find an inverted-U relation between Accruals or net operating assets (NOA) and subsequent one-year abnormal returns. They argue that this opposes behavioral explanations for the Accrual and NOA anomalies. We show that the inverted-U relation is a spurious consequence of the truncation bias noted in Kothari, Sabino, and Zach (2005). LTS trimming for these anomalies effectively trims observations by the value of the dependent variable (returns). We show that because returns skewness varies systematically with the accounting predictor, the LTS trimming induces a truncation bias that varies systematically across the accounting predictors. The variation in returns skewness is related to the variation in the incidence of loss firms across the accounting predictors. Among profit firms, which have less skewed returns and so are less subject to the truncation bias, the negative monotonic relation between accounting predictors and subsequent abnormal returns is robust to trimming. Thus, ex post non-random trimming of returns can spuriously induce evidence against either the efficient market hypothesis or behavioral theories. Additionally, this paper shows that the anomalies survive trimming, despite the truncation bias, when a larger set of asset pricing controls and test methods that control for cross-sectional dependence are used.

Instantaneous 3D motion from image derivatives using the Least Trimmed Square regression

This paper presents a new technique to the instantaneous 3D motion estimation. The main contributions are as follows. First, we show that the 3D camera or scene velocity can be retrieved from image derivatives only assuming that the scene contains a dominant plane. Second, we propose a new robust algorithm that simultaneously provides the Least Trimmed Square solution and the percentage of inliers—the non-contaminated data. Experiments on both synthetic and real image sequences demonstrated the effectiveness of the developed method. Those experiments show that the new robust approach can outperform classical robust schemes.

Face recognition from 2D and 3D images using 3D Gabor filters

To recognize faces with different facial expressions or varying views from only one stored prototype per person is challenging. This paper presents such a system based on both 3D range data as well as the corresponding 2D gray-level facial images. The traditional 3D Gabor filter (3D TGF) is explored in the face recognition domain to extract expression-invariant features. To extract view-invariant features, a rotation-invariant 3D spherical Gabor filter (3D SGF) is proposed. Furthermore, a two-dimensional (2D) Gabor histogram is employed to represent the Gabor responses of the 3D SGF for solving the missing-point problem caused by self-occlusions under large rotation angles. The choice of 3D Gabor filter parameters for face recognition is examined as well. To match a given test face with each model face, the Least Trimmed Square Hausdorff Distance (LTS-HD) is employed to tackle the possible partial-matching problem. Experimental results based on our face database involving 80 persons have demonstrated that our approach outperforms the standard Eigenface approach and the approach using the 2D Gabor-wavelets representation.

효과적인 영상처리를 위한 α-LTSHD 기반의 FCNN 구조 연구

본 논문에서, 영상에서 임펄스 잡음을 효과적으로 제거하고, 연산 속도를 개선하기 위해 Fuzzy Cellular Neural Network(FCNN)구조에 Hausdorff distance(HD)를 적용한 <TEX>$\alpha$</TEX>-Least Trimmed Square HD(<TEX>$\alpha$</TEX>-LTSHD) 기반 FCNN 구조를 제안한다. FCNN는 Cellular Neural Network(CNN) 구조에 퍼지 이론을 적용한 것이고, HD는 특징 대상의 대응 없이 이진 영상의 두 픽셀 집합 사이의 거리를 구하는 척도로 물체의 정합에 널리 사용한다. 성능 평가를 위해, 제안된 방법을 MSE와 SNR을 이용하여 기존 FCNN, Opening-Closing(OC) 그리고 LTSHD 연산자를 적용한 FCNN과 비교 분석하였다. 그 결과, 본 논문에서 제안된 망(network) 구조의 성능이 다른 필터보다 임펄스 잡음 제거에 우수함을 확인하였다. In this paper, we propose a Fuzzy Cellular Neural Network(FCNN) that is based on a-Least Trimmed Square Hausdorff distance(a-LTSHD) which applies Hausdorff distance(HD) to the FCNN structure in order to remove the impulse noise of images effectively and also improve the speed of operation. FCNN incorporates Fuzzy set theory to Cellular Neural Network(CNN) structure and HD is used as a scale which computes the distance between set or two pixels in binary images without confrontation of the feature object. This method has been widely used with the adjustment of the object. For performance evaluation, our proposed method is analyzed in comparison with the conventional FCNN, with the Opening-Closing(OC) method, and the LTSHD based FCNN by using Mean Square Error(MSE) and Signal to Noise Ratio(SNR). As a result, the performance of our proposed network structure is found to be superior to the other algorithms in the removal of impulse noise.