Regression with outlier shrinkage

The demand for healthcare facilities in the world is growing daily, and this growth in demand exceeds general population growth. This situation has made hospital trips a vital issue during urban transportation planning. In this context, the aim of this study is twofold: (1) to investigate the hospital trip behavior as home-based hospital trips within the scope of trip production and attraction (trip generation) models and (2) to evaluate the predictive power of some robust and regularization methods in trip generation modeling. Within this scope, approximately 49,000 valid Household Survey Data (HSD) from 2001 (base year) and 2015 (target year) were used to develop comprehensive trip generation models for the home-based hospital trips. Multiple linear regression (MLR), ridge regression (RR), Liu, least trimmed squares (LTS), least trimmed squares–ridge (LTS–R), and least trimmed square–Liu (LTS–L) methods were used for the analysis, and results were evaluated in terms of specialized mean squared error (MSE) and root mean square error (RMSE). As a result, LTS–R and LTS–L increased future predictive power by approximately 55% compared with OLS. This study fills an important gap in the literature in terms of not only the use of regularization and robust methods in trip demand modeling but also examining characteristics that affect hospital trip behaviors. In addition, the paper proposes a “Hospital Mobility Coefficient” projection that could be useful in demand estimation for future hospital trips.

Fast and robust bootstrap for LTS

Robust principal component regression is development of principal component regression that applies robust method at principal component analysis and principal component regression analysis. Robust principal component regression does not only overcome multicollinearity problems, but also overcomes outlier problems. The robust methods used in this research are Minimum Covariance Determinant (MCD) that is applied when doing principal component analysis and Least Trimmed Squares (LTS) that is applied when doing principal component regression analysis. The case study in this research is Human Development Index (HDI) in Central Java in 2017 which is influenced by labor force participation rates, school enrollment rates, percentage of poor population, population aged 15 years and over who are employed, health facilities, gross enrollment rates, and net enrollment rates. The model of HDI in Central Java in 2017 using robust principal component regression MCD-LTS provides the most effective result for handling multicollinearity and outliers with Adjusted R2 value of 0.6913 and RSE value of 0.469. Keywords: Robust Principal Component Regression, Multicollinearity, Outliers, Minimum Covariance Determinant (MCD), Least Trimmed Squares (LTS), Human Development Index (HDI).

This paper is focusing on the application of robust method in multiple linear regression (MLR) model towards diabetes data. The objectives of this study are to identify the significant variables that affect diabetes by using MLR model and using MLR model with robust method, and to measure the performance of MLR model with/without robust method. Robust method is used in order to overcome the outlier problem of the data. There are three robust methods used in this study which are least quartile difference (LQD), median absolute deviation (MAD) and least-trimmed squares (LTS) estimator. The result shows that multiple linear regression with application of LTS estimator is the best model since it has the lowest value of mean square error (MSE) and mean absolute error (MAE). In conclusion, plasma glucose concentration in an oral glucose tolerance test is positively affected by body mass index, diastolic blood pressure, triceps skin fold thickness, diabetes pedigree function, age and yes/no for diabetes according to WHO criteria while negatively affected by the number of pregnancies. This finding can be used as a guideline for medical doctors as an early prevention of stage 2 of diabetes.

The incorporation of the robust regression methods Least Median Square (LMS) and Least Trimmed Squares (LTS) is proposed in structural equation modeling. Results show that, in situations of high deviations of symmetry, the evaluated methods would be recommended for applications including smaller sample sizes.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a robust calibration procedure for clustered wireless sensor networks. Accurate calibration of between-node distances is one crucial step in localizing sensor nodes in an ad-hoc sensor network. The calibration problem is formulated as a parameter estimation problem using a linear calibration model. For reducing or eliminating the unwanted influence of measurement corruptions or outliers on parameter estimation, which may be caused by sensor or communication failures, a robust regression estimator such as the least-trimmed squares (LTS) estimator is a natural choice. Despite the availability of the FAST-LTS routine in several statistical packages (e.g., R, S-PLUS, SAS), applying it to the sensor network calibration is not a simple task. To use the FAST-LTS, one needs to input a trimming parameter, which is a function of the sensor redundancy in a network. Computing the redundancy degree and subsequently solving the LTS estimation both turn out to be computationally demanding. Our research aims at utilizing some cluster structure in a network configuration in order to do robust estimation more efficiently. We present two algorithms that compute the exact value and a lower bound of the redundancy degree, respectively, and an algorithm that computes the LTS estimation. Two examples are presented to illustrate how the proposed methods help alleviate the computational demands associated with robust estimation and thus facilitate robust calibration in a sensor network. </para>

Generalized least-squares and maximum likelihood approaches for parameter estimation in multivariate response models have been prevalent in the chemical kinetics literature to date. In contrast, robust alternatives have received considerably less attention. These methods safeguard against possible deviations from the assumptions, such as the presence of outliers or non-normality of the random errors. We compare, through Monte Carlo simulation, the performance of the classical Box–Draper determinant criterion (ML) to those of two robust estimators: the multivariate Huber’s M-estimator and the multivariate least-trimmed squares estimator (MLTS). Although the results are not entirely conclusive, overall, we find no compelling evidence for preferring any one of the two robust methods over the conventional ML estimates. At the same time, it was unexpected to find that ML is still reasonable under mild outlier contamination and mild deviations from normality. This notwithstanding, one loses nothing by comparing ML together with MLTS to cross-check each other as a safety measure.

In the multiple linear regression analysis, the ridge regression estimator and the Liu estimator are often used to address multicollinearity. Besides multicollinearity, outliers are also a problem in the multiple linear regression analysis. We propose new biased estimators based on the least trimmed squares (LTS) ridge estimator and the LTS Liu estimator in the case of the presence of both outliers and multicollinearity. For this purpose, a simulation study is conducted in order to see the difference between the robust ridge estimator and the robust Liu estimator in terms of their effectiveness; the mean square error. In our simulations, the behavior of the new biased estimators is examined for types of outliers: X-space outlier, Y-space outlier, and X-and Y-space outlier. The results for a number of different illustrative cases are presented. This paper also provides the results for the robust ridge regression and robust Liu estimators based on a real-life data set combining the problem of multicollinearity and outliers.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

Summary In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust estimator such as the least median of squares (LMS) or least trimmed squares (LTS) or for example the more recent MM estimators of Yohai. Such estimators are now standard in statistics computing packages, for example as in SPLUS or R. In addition to the asymptotics we provide data analyses supporting the new adaptive approach. This approach appears to work well on a number of data sets and is quicker than the related brute force adaptive regression approach described in Clarke (2000). This current approach builds on the work of Bednarski and Clarke (2002) which considered the asymptotics for the location estimator only.

Ordinary Least Squares (OLS) is one method of parameter estimation in regression analysis. However, the presence of outliers can cause estimation of regression coefficients obtained are not exact. Act of throwing away an outlier is not a wise move, because sometimes outliers provide significant information. Therefore, robust regression methods are needed to data contain outliers. This paper will use robust regression estimation method by M-estimation. This estimation use Iteratively Reweighted Least Squares (IRLS) method with weighting function by Huber and Tukey Bisquare. IRLS is applied to the case of food security in Central Java in 2007 that is influenced by the stock of rice, harvested area, average production, price of rice and the amount of consumption. The purpose of this writing is to compare goodness of M-estimation IRLS using Huber and Tukey Bisquare function in estimating the model parameters of food security in Central Java in 2007. Based on the research results can be concluded that the M-estimation by the Tukey Bisquare is better recommended than Huber function. This can be seen by value results of Mean Square Error and determination coefficient

Robust Multivariate Statistical Methods

To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore, it can be used to compute the asymptotic variance and the mean-squared error (MSE). In this paper we compute the influence function, the asymptotic variance and the MSE for penalized M-estimators and the sparse LTS estimator. The asymptotic biasedness of the estimators make the calculations non-standard. We show that only M-estimators with a loss function with a bounded derivative are robust against regression outliers. In particular, the lasso has an unbounded influence function.

Unemployment is one of the most important issues in macro economics. Unemployment creates many economic and social problems in the economy. The condition and qualification of labor force in a country show economical developments. In the light of these facts, a developing country should overcome the problem of unemployment. In this study, the performance of robust biased Robust Ridge Regression (RRR), Robust Principal Component Regression (RPCR) and RSIMPLS methods are compared with each other and their classical versions known as Ridge Regression (RR), Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR) in terms of predictive ability by using trimmed Root Mean Squared Error (TRMSE) statistic in case of both of multicollinearity and outliers existence in an unemployment data set of Turkey. Analysis results show that RRR model is chosen as the best model for determining unemployment rate in Turkey for the period of 1985-2012. Robust biased RRR method showed that the most important independent variable effecting the unemployment rate is Purchasing Power Parities (PPP). The least important variables effecting the unemployment rate are Import Growth Rate (IMP) and Export Growth Rate (EXP). Hence, any increment in PPP cause an important increment in unemployment rate, however, any increment in IMP causes an unimportant increase in unemployment rate. Any increment in EXP causes an unimportant decrease in unemployment rate.

The variation of background harmonics, system harmonic impedance and load characteristics will affect the harmonic voltage and current at the point of common coupling(PCC), which will lead to large estimation error of harmonic contribution if ignored. In this paper, a simple and effective method is proposed to identify the abrupt transition points in the harmonic parameter data, then the harmonic voltage and current data are divided into several stable data sections, in which the background harmonic and system harmonic impedance are basically unchanged, and the load characteristics are relatively stable. On this basis, the harmonic contribution of the harmonic source is discussed and evaluated by using the robust regression method in the data segment, and the dynamic variation of the harmonic contribution parameter in the time period is obtained. The simulation results show that the proposed method can accurately identify the variation of harmonic parameters and divide the harmonic information into several stable data segments. The robust regression method has higher accuracy than other linear regression methods. The accuracy and effectiveness of the proposed method are proved.