Problem Of Outliers Research Articles

English

Recently, there is strong interest on the subject of outlier problem in circular data. In this paper, we focus on detecting outliers in a circular regression model proposed by Down and Mardia. The basic properties of the model are available including the exact form of covariance matrix of the parameters. Hence, we intend to identify outliers in the model by looking at the effect of the outliers on the covariance matrix. The method resembles closely the COVRATIO statistic for the case of linear regression problem. The corresponding critical values and the performance of the outlier detection procedure are studied via simulations. For illustration, we apply the procedure on the wind data set.

Robust Liu-type estimator for regression based on M-estimator

ABSTRACTThe problem of multicollinearity and outliers in the dataset can strongly distort ordinary least-square estimates and lead to unreliable results. We propose a new Robust Liu-type M-estimator to cope with this combined problem of multicollinearity and outliers in the y-direction. Our new estimator has advantages over two-parameter Liu-type estimator, Ridge-type M-estimator, and M-estimator. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.

A Robust Test for Threshold‐Type Nonlinearity in Multivariate Time Series Analysis

There is growing interest in exploring potential forecast gains from the nonlinear structure of multivariate threshold autoregressive (MTAR) models. A least squares‐based statistical test has been proposed in the literature. However, previous studies on univariate time series analysis show that classical nonlinearity tests are often not robust to additive outliers. The outlier problem is expected to pose similar difficulties for multivariate nonlinearity tests. In this paper, we propose a new and robust MTAR‐type nonlinearity test, and derive the asymptotic null distribution of the test statistic. A Monte Carlo experiment is carried out to compare the power of the proposed test with that of the least squares‐based test under the influence of additive time series outliers. The results indicate that the proposed method is preferable to the classical test when observations are contaminated by outliers. Finally, we provide illustrative examples by applying the statistical tests to two real datasets. Copyright © 2015 John Wiley & Sons, Ltd.

Testing of Suspected Observations in an Exponential Sample With Unknown Origin

The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.

Robust model selection criteria for robust S and LTS estimators

Outliers and multi-collinearity often have large influence in the model/variable selection process in linear regression analysis. To investigate this combined problem of multi-collinearity and outliers, we studied and compared Liu-type S (liuS-estimators) and Liu-type Least Trimmed Squares (liuLTS) estimators as robust model selection criteria. Therefore, the main goal of this study is to select subsets of independent variables which explain dependent variables in the presence of multi-collinearity, outliers and possible departures from the normality assumption of the error distribution in regression analysis using these models.

An improved ensemble learning machine for biological activity prediction of tyrosine kinase inhibitors

Boosting is one of the most important strategies in ensemble learning because of its ability to improve the stability and performance of weak learners. It is nonparametric, multivariate, fast and interpretable but is not robust against outliers. To enhance its prediction accuracy as well as immunize it against outliers, a modified version of a boosting algorithm (AdaBoost R2) was developed and called AdaBoost R3. In the sampling step, extremum samples were added to the boosting set. In the robustness step, a modified Huber loss function was applied to overcome the outlier problem. In the output step, a deterministic threshold was used to guarantee that bad predictions do not participate in the final output. The performance of the modified algorithm was investigated with two anticancer data sets of tyrosine kinase inhibitors, and the mechanism of inhibition was studied using the relative weighted variable importance procedure. Investigating the effect of base learner's strength reveals that boosting is only successful using the classification and regression tree method (a weak to moderate learner) and does not have a significant effect using the radial basis functions partial least square method (a strong base learners). Copyright © 2015 John Wiley & Sons, Ltd.

TRADE SPECIALIZATION INDICES: TWO COMPETING MODELS

Revealed Comparative Advantage (RCA) index by Balassa (1965) is intensively applied in empirical studies on countries’ comparative advantage or trade specialization. Asymmetric problem in the criteria of RCA index encourages Dalum et al. (1998) and Laursen (1998) to make Revealed Symmetric Comparative Advantage (RSCA) index. These two indexes are commonly employed in econometric models for analyzing countries’ trade specialization. This paper aims to compare theoretically and empirically the two competing econometric models, one using RCA and the other using RSCA. The ASEAN countries’ comparative advantages are presented for the empirical case studies. This paper concludes that RSCA can, to some extent, reduce the “outlier problem” of RCA in the econometric model; therefore, the model using RSCA can be more statistically reliable than the model using RCA. The two econometric models might not be suitable for forecasting purposes since the estimated values could theoretically violate their criteria of comparative advantage and disadvantage. In the cases of ASEAN countries, we find empirically that the model using RSCA is statistically more reliable than the one using RCA. The ASEAN countries have exhibited de-specialization. JEL classification: F10, F14, F17 Keywords: Revealed Comparative Advantage (RCA), Revealed Symmetric Comparative Advantage (RSCA).

Efficiency and productivity of the cement industry: Pakistani experience of deregulation and privatisation

This study evaluates the impact of privatisation on efficiency and productivity of the Pakistani cement industry. To address some of the serious concerns about the problem of dimension and outlier, we use a newly developed unconditional hyperbolic α-quantile estimator of Wheelock and Wilson to estimate efficiency (Wheelock DC, Wilson PW. Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations. Journal of Econometrics; 2008: 209–25). Subsequently, we use these efficiency estimates to calculate the Malmquist productivity growth and its components. The results show that deregulation and privatisation had the desired positive effect on productivity growth due to technological progress. We conclude that this improvement in the post reform period could be linked to political stability, improved economic conditions and a competitive industry.

Robust two parameter ridge M-estimator for linear regression

The problem of multicollinearity and outliers in the data set produce undesirable effects on the ordinary least squares estimator. Therefore, robust two parameter ridge estimation based on M-estimator (ME) is introduced to deal with multicollinearity and outliers in the y-direction. The proposed estimator outperforms ME, two parameter ridge estimator and robust ridge M-estimator according to mean square error criterion. Moreover, a numerical example and a Monte Carlo simulation experiment are presented.

Looking for a Needle in a Haystack: Revisiting the Cross‐country Causes of the 2008–9 Crisis by Bayesian Model Averaging

In this paper we explore the cross‐country variation in the output impact of the global financial crisis in 2008–9. We use the extensive dataset of Rose and Spiegel but control for the problems of model uncertainty and outliers by using a variety of Bayesian model averaging techniques. We find first that cross‐country differences in crisis intensity can be explained by macroeconomic vulnerabilities. Second, ignoring model uncertainty can lead to incorrect inferences. Third, international trade linkages do matter.

Using Ridge Least Median Squares to Estimate the Parameter by Solving Multicollinearity and Outliers Problems

In the multiple linear regression analysis, the ridge regression estimator is often used to address the problem of multicollinearity. Besides multicollinearity, outliers also constitute a problem in the multiple linear regression analysis. We propose a new biased estimators of the robust ridge regression called the Ridge Least Median Squares (RLMS) estimator in the presence of multicollinearity and outliers. For this purpose, a simulation study is conducted in order to see the difference between the proposed method and the existing methods in terms of their effectiveness measured by the mean square error. In our simulation studies the performance of the proposed method RLMS is examined for different number of observations and the different percentage of outliers. The results of different illustrative cases are presented. This paper also provides the results of the RLMS on a real-life data set. The results show that RLMS is better than the existing methods of Ordinary Least Squares (OLS), Ridge Least Absolute Value (RLAV) and Ridge Regression (RR) in the presence of multicollinearity and outliers.

Data Calibration Based on Multisensor Using Classification Analysis: A Random Forests Approach

This paper analyzes the problem of meaningless outliers in traffic detective data sets and researches characteristics about the data of monophyletic detector and multisensor detector based on real-time data on highway. Based on analysis of the current random forests algorithm, which is a learning algorithm of high accuracy and fast speed, new optimum random forests about filtrating outlier in the sample are proposed, which employ bagging strategy combined with boosting strategy. Random forests of different number of trees are applied to analyze status classification of meaningless outliers in traffic detective data sets, respectively, based on traffic flow, spot mean speed, and roadway occupancy rate of traffic parameters. The results show that optimum model of random forest is more accurate to filtrate meaningless outliers in traffic detective data collected from road intersections. With filtrated data for processing, transportation information system can decrease the influence of error data to improve highway traffic information services.

Robust Stability Best Subset Selection for Autocorrelated Data Based on Robust Location and Dispersion Estimator

Stability selection (multisplit) approach is a variable selection procedure which relies on multisplit data to overcome the shortcomings that may occur to single-split data. Unfortunately, this procedure yields very poor results in the presence of outliers and other contamination in the original data. The problem becomes more complicated when the regression residuals are serially correlated. This paper presents a new robust stability selection procedure to remedy the combined problem of autocorrelation and outliers. We demonstrate the good performance of our proposed robust selection method using real air quality data and simulation study.

A NEW CLASS OF ADAPTIVE CFAR METHODS FOR NONHOMOGENEOUS ENVIRONMENTS

The paper introduces a new class of adaptive CFAR methods to cope with the problem of outliers due to the presence of clutter edges and interfering targets. A fundamental distinction between the proposed approach and existing adaptive CFAR approaches is that in order to maintain robust performance the former uses information on positions at which estimated outlier-free cells appear in the full reference window and the statistics of the sample in the cell under test. The performance of one of the possible implementations of new adaptive CFAR methods is studied and compared with that of an existing adaptive CFAR approach. The results show signiflcant advantages of the proposed class of adaptive CFAR methods in both the false alarm regulation property and detection performance.

Robust Weighted Least Squares Estimation of Regression Parameter in the Presence of Outliers and Heteroscedastic Errors

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affected by outliers. To remedy this, We have suggested a strong technique for the estimation of regression parameters in the existence of heteroscedasticity and outliers. Here we apply the robust regression of M-estimation using iterative reweighted least squares (IRWLS) of Huber and Tukey Bisquare function and resistance regression estimator of least trimmed squares to estimating the model parameters of state-wide crime of united states in 1993. The outcomes from the study indicate the estimators obtained from the M-estimation techniques and the least trimmed method are more effective compared with those obtained from the OLS.

Early automatic detection of Parkinson's disease based on sleep recordings.

Idiopathic rapid-eye-movement (REM) sleep behavior disorder (iRBD) is most likely the earliest sign of Parkinson's Disease (PD) and is characterized by REM sleep without atonia (RSWA) and consequently increased muscle activity. However, some muscle twitching in normal subjects occurs during REM sleep. There are no generally accepted methods for evaluation of this activity and a normal range has not been established. Consequently, there is a need for objective criteria. In this study we propose a full-automatic method for detection of RSWA. REM sleep identification was based on the electroencephalography and electrooculography channels, while the abnormal high muscle activity was detected from the electromyography channels, in this case the submentalis combined with left and right anterior tibialis. RSWA was identified by considering it an outlier problem, in which the number of outliers during REM sleep was used as a quantitative measure of muscle activity. The proposed method was able to automatically separate all iRBD test subjects from healthy elderly controls and subjects with periodic limb movement disorder. The proposed work is considered a potential automatic method for early detection of PD.

대학도서관 통계분석을 통한 대학도서관 성과 및 영향요인에 대한 연구

본 연구는 한국교육학술정보원(KERIS)이 운영하는 학술정보통계시스템(rinfo.kr)의 2010-2013년간 대학도서관통계를 대상으로 지속가능성에 기반한 경영자원 확보를 성과요소로 한 탐색적 통계분석을 목표로 한다. 이를 위해 선행되는 영향요소 및 후행되는 성과요소를 고려하고 규모 및 사회경제적인 외부변인들을 통제하기 위한 변화율 중심의 변수를 산출하는 전처리 방법을 통계에 적용하였으며, 이를 통한 변수를 대상으로 요인분석과 회귀분석을 실시하였다. 요인분석 결과 13개의 요인을 추출할 수 있었으며, 회귀분석 결과 대학도서관 경영자원 확보에 영향을 미치는 변수를 확인하였다. 분석결과를 바탕으로 극단값의 문제, 변수 간 낮은 상관성, 그리고 낮은 효과크기를 배경으로 한 새로운 변수의 개발을 논의하였다. 본 연구를 통해 지속가능성에 기반한 대학도서관의 통계체계, 평가, 나아가 경영에 대한 논의가 확산되기를 기대한다. The goal of this study is an exploratory statistical analysis of the university and college library statistics in the Academic Information Statistics System(rinfo.kr) governed of Korean Education and Research Information Service(KERIS) with performance measures based on sustainability. For the goal, we adopt a preprocessing method to develop change-rate variables by considering preceding predictive elements and succeeding performance elements, and to control external factors, such as size and socioeconomic factors. Then we execute a series of factor analyses and multiple linear regression analyses. 13 factors are extracted by the factor analyses and some sets of significant variables affecting the performance measures are identified through the regression analyses. Based on the results, we discuss the problem of out-lier and low correlation between variables. A suggestion for developing new variables is also discussed based on low effect sizes of the developed regression models. We hope that this study contributes to diffuse discussions on statistics system, evaluation, and further library management based on sustainability.

Robust Estimation of Parameters in Simple Linear Profiles Using M-Estimators

In many situations, the quality of a process or product may be better characterized and summarized by a relationship between the response variable and one or more explanatory variables. Parameter estimation is the first step in constructing control charts. Outliers may hamper proper classical estimators and lead to incorrect conclusions. To remedy the problem of outliers, robust methods have been developed recently. In this article, a robust method is introduced for estimating the parameters of simple linear profiles. Two weight functions, Huber and Bisquare, are applied in the estimation algorithm. In addition, a method for robust estimation of the error terms variance is proposed. Simulation studies are done to investigate and evaluate the performance of the proposed estimator, as well as the classical one, in the presence and absence of outliers under different scenarios by the means of MSE criterion. The results reveal that the robust estimators proposed in this research perform as well as classical estimators in the absence of outliers and even considerably better when outliers exist. The maximum value of variance estimate in one scenario obtained from classical estimator is 10.9, while this value is 1.66 and 1.27 from proposed robust estimators when its actual value is 1.

M-estimator based unit root tests in the ESTAR framework

Building on work of Lucas (Econom Theory 11:331–346, 1995a) we derive the limiting distribution for M-estimator based unit root tests in the ESTAR model. This yields that the LS based unit root tests by Kapetanios et al. (J Econom 112:359–379, 2003) and Rothe and Sibbertsen (Allg Stat Arch 90:439–456, 2006) are robustified in an outlier context. We also consider an LS based heteroscedasticity robust version (White’s) of one of our unit root tests as a “quick fix” solution to the problems of outliers. Finite sample properties of the tests are examined, and in the case of additive outliers it is shown that the LS based tests are grossly over-sized whereas the size of our tests is close to the nominal size. If an ESTAR model with innovation outliers is considered, significant power gains over the LS based tests are shown by using our robust tests.

The normalized interval regression model with outlier detection and its real-world application to house pricing problems

Tanaka and his colleagues initially proposed fuzzy linear regression models in 1982. From then on, fuzzy regression analysis has been widely studied by many researchers. Since Tanaka's model uses the inclusion relationship between the given data and the estimated data, it was pointed out that Tanaka's model is sensitive to outliers. How to deal with the outlier problem has been a very important issue and attracted much attention from fuzzy regression researchers. Given crisp multiple independent variables and single interval dependent variable, we introduce the normalized upper and lower interval regression models and propose two outlier detection approaches for them. The dual problem of the normalized upper interval regression model is used to find out potential outliers. For the normalized lower interval regression model, the existence of the outliers makes it infeasible. The relaxation approach is proposed to find out the outliers. By deleting the outliers, we can find out the possibilistic functional relationship of the major data. A case study involving a house pricing problem is analyzed in detail. Household size, loan ratio and annual household income are identified as the independent variables and acceptable purchase price is the interval dependent variable. With the data collected from the survey in Shanghai, the normalized upper and lower interval regression models are built with deleting the outliers. The proposed models provide managerial insights into the real estate market and important policy implications in regulating urban land development.