Robust Linear Regression Methods Research Articles

Identification of Photovoltaic Array Model Parameters by Robust Linear Regression Methods

The aim of this paper is to propose an approach for photovoltaic (PV) sources modeling based on robust least squares linear regression (LSR) parameter identification method. On the basis of experimental data of solar irradiance, cell temperature and voltage and currents at maximum power points for a given PV array, correlation functions among the considered quantities are defined. By implementing these functions in a Matlab® Simulink model, accurate I-V characteristics for the considered array are obtained, managing only the solar irradiance. The method is validated comparing the computed and the experimental maximum power points (MPPs). Its effectiveness is proven to be better with respect of parameter identification methods based on discrete approaches and standard LSR method

Interval joint robust regression method

Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. A number of regression methods suitable to interval variables describing variability of complex objects are already available. However, less attention has been given to methods that, simultaneously, take into account the full interval information and are resistant to interval outlier observations, even with the frequent presence of atypical observations on interval-valued data sets. This paper proposes a new robust linear regression method for interval variables, where the presence of outliers either in the center or in the radius penalize both the center and the radius regression models. Moreover, the interval observations with outliers on both center and radius are more penalized than those observations with outliers only in the center (or in the radius). Besides, this paper provides a suitable iterative algorithm to estimate the parameters of the proposed method. The algorithm estimates the parameters of the center (or of the radius) model taking into account both information of the center and the radius. The convergence and time complexity of the iterative algorithm are also presented. Finally, the performance of the new method is compared with some previous robust regression approaches and evaluated on synthetic and real interval-valued data sets.

Non-surgical correction of cryptotia and the analysis of treatment time and other influence factors

ObjectiveTo explore correlations between post-treatment outcomes of non-surgical correction for cryptotia and treatment time and other influence factors. MethodsForty-seven consecutive patients with 64 cryptotias were treated with the adjusted external stretching device and followed up over 12 months. A subjective evaluation scale was designed for patients to collect clinical data. Pretreatment and posttreatment evaluation were conducted by two blinded investigators. The correlations between influence factors and outcomes were explored through fractional polynomial method, multiple logistic regression, and robust linear regression methods. ResultsThirty-five patients with 49 cryptotias were included. Twenty-nine cryptotias (23 patients) have been successfully managed. Two of 17 unilateral cryptotias achieved nearly complete symmetry. The final optimal cutoff value for initiating treatment time is 6 months and for the duration of treatment per day is 5 h per day. Positive relationships between initiating treatment time >6 months and onset time, type II and onset time, initiating treatment time >6 months and effect stabilization time were observed. ConclusionsInitiating treatment time <6 months and duration of treatment per day >5 h benefit for the posttreatment outcomes. Patients wearing the device under 6 months old would have earlier onset time and effect stabilization time. It is hard to achieve complete bilateral symmetry in unilateral patients. The adjustable devices can used for the auricles with different sizes and removed and equipped conveniently.

Association between genome‐wide DNA methylation pattern and response to trastuzumab in HER2‐positive breast cancer patients

IntroductionThe administration of trastuzumab has led to significant improvement in survival of HER2‐positive breast cancer patients in the adjuvant and metastatic settings. Trastuzumab resistance, however, has been increasingly recognized as a major obstacle. Recent evidence suggests that epigenetic mechanisms might be associated with acquired resistance to cancer therapies. Aim of this study was to explore the association between genome‐wide DNA methylation pattern in breast cancer tissue and the response to trastuzumab.Patients and methodsDNA methylation pattern was assessed in breast cancer tissues of trastuzumab‐treated HER2‐positive breast cancer patients who acquired resistance to treatment (case group, n=6) and compared to that of trastuzumab‐treated HER2‐positive breast cancer patients who did not develop resistance (control group, n=6) using the Illumina Infinium HumanMethylation450 BeadChip. Cases were matched to controls for several factors. Bioinformatics analyses were performed using the R statistical environment (robust linear regression method) to identify differentially methylated genes (DMGs) (FDR &lt; 0.05) between case and control groups.ResultsCompared to the control group, in the matched case group we identified 879 hypermethylated and 293 hypomethylated genes. The differentially methylated set of genes was enriched in molecular and cellular functions associated with cellular movement (P=8.02E‐07) as well as cell death and survival (P=4.24E‐09). Pathways associated with ERK/MAPK signaling and regulation of the epithelial‐mesenchymal transition were overrepresented (P=2.13E‐05, and P=2.43E‐03, respectively). Among the DMGs we observed AGPAT1, a gene related to the PI3K‐mTOR pathway which has been reported to be implicated with trastuzumab resistance in addition to be differentially expressed between HER2‐positive breast cancer patients who responded to trastuzumab and those who acquired resistance.ConclusionsAlthough our sample size was small, we observed DMGs associated with the response to trastuzumab. These data need to be confirmed in a larger prospective cohort of trastuzumab‐treated HER2‐positive breast cancer patients.Support or Funding InformationDF received doctoral fellowships from the Fonds de recherché du Québec – Santé (FRQS) and the Laval University Cancer Research Center. CD is a recipient of the Canadian Breast Cancer Foundation‐Canadian Cancer Society Development award (award #703003) and the FRQS Research Scholar.This study was supported by the Fondation des Hôpitaux Enfant Jésus – St‐Sacrement. Clinical specimens were provided by the Fondation du cancer du sein du Québec and the Banque de tissus et de données of the Réseau de recherche sur le cancer of the FRQS, which is affiliated with the Canadian Tumour Repository Network.This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Comparative the performance of robust linear regression methods and its application

Comparative the performance of robust linear regression methods and its application

Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions.

Comparison of Robust Methods for Shear Wave Speed Estimation by Simulation

Mechanical properties of tissue are often related to the pathological state of tissue. Therefore, non-invasively measuring tissue stiffness has important clinical applications. With the assumption of isotropy, incompressibility and linearity, the shear modulus of tissue is related to its shear wave propagation speed. Acoustic radiation force from a focused ultrasound beam can be used to generate shear waves at the focal region within tissue, which propagate orthogonally to the direction of the pushing ultrasound beam. The shear wave speed can be estimated based on the so called time-to-flight principle. The shear wave arrival time determined at several lateral positions along the shear wave propagation path can be measured by the displacement profiles, which can be tracked using correlation-based method by pulse-echo ultrasound. This approach has been successively used with various modifications by several groups. The purpose of this study is to design a simulation method to generate the pulse-echo ultrasound signal, calculate the displacement profile in the spatial and time domain, and estimate the shear wave speed using RANSAC, Radon Sum and robust linear regression method, compare and analyze the algorithm performance of these methods.

TELBS robust linear regression method

TELBS robust linear regression method MA Tabatabai,1 WM Eby,1 H Li,1 S Bae,2 KP Singh21Department of Mathematical Sciences, Cameron University, Lawton, OK, 2Department of Medicine, University of Alabama, Birmingham, AL, USAAbstract: Ordinary least squares estimates can behave badly when outliers are present. An alternative is to use a robust regression technique that can handle outliers and influential observations. We introduce a new robust estimation method called TELBS robust regression method. We also introduce a new measurement called Sh(i) for detecting influential observations. In addition, a new measure for goodness of fit, called R2RFPR, is introduced. We provide an algorithm to perform the TELBS estimation of regression parameters. Real and simulated data sets are used to assess the performance of this new estimator. In simulated data with outliers, the TELBS estimator of regression parameters performs better in comparison with least squares, M and MM estimators, with respect to both bias and mean squared error. For rat liver weights data, none of the estimators (least squares, M, and MM) are able to estimate the parameters accurately. However, TELBS does give an accurate estimate. Using real data for brain imaging, the TELBS and MM methods were equally accurate. In both of these real data sets, the Sh(i) measure was very effective in identifying influential observations. The robustness and simplicity of computations of TELBS model parameters make this method an appropriate one for analysis of linear regression. Algorithms and programs have been provided for ease in implementation, including all relevant statistics necessary to perform a complete analysis of linear regression.Keywords: robust linear regression, least squares estimator, M and MM estimators, magnetic resonance imaging, Cook&#39;s distance, detection of influential observations, Studentized residual

An inferential modeling method using enumerative PLS based nonnegative garrote regression

In this paper a robust linear regression method with variable selection is proposed for predicting desirable end-of-line quality variables in complex industrial processes. The development of such prediction models is challenging because there is usually a large pool of candidate explanatory variables, limited sample data, and multicollinearity among explanatory variables. The proposed method is named as the enumerative partial least square based nonnegative garrote regression. It employs partial least square regression in enumerative manner to generate initial model coefficients and then uses a nonnegative garrote method to shrink original coefficients so that irrelevant variables can be eliminated implicitly. Analysis about the advantages of the proposed method is provided compared to existing state-of-art model construction methods. Two simulation examples as well as an industrial application in a local semiconductor factory unit are used to validate the proposed method. These examples witness substantial improvement in terms of accuracy and robustness in variable selection compared to existing methods. Specifically, for the industrial case the percentages of improvement in terms of root mean squared error is up to 24.3% compared with the previous work.

Meteorologically Adjusted Ground Level Ozone Trends in Southern Taiwan

Two methods were used to calculate the meteorologically adjusted ground level ozone trends in southern Taiwan. The first method utilized is a robust linear regression method. The second approach uses a multilayer perceptron (MLP) artificial neural network (ANN) method. The observations obtained from 16 monitoring stations were analyzed and divided into six groups by hierarchical divisive clustering procedure. The daily maximum 1 and 8 h ozone concentrations for each group are then calculated. The meteorologically adjusted trends obtained by linear regression and MLP methods are smaller than the unadjusted trends for all groups and average time. It indicts that the meteorological conditions in Taiwan tend to increase ambient ozone concentrations in recent years.

Racial Differences in Premenopausal Endogenous Hormones

Differences in breast cancer incidence across racial groups are well documented. African Americans have the highest rates of premenopausal breast cancer and Asians have lower breast cancer rates across all age groups. We hypothesized that levels of premenopausal endogenous hormones and growth factors, risk factors that have been predictive of breast cancer, would differ by race. Using a cross-sectional study design, we tested this hypothesis in the Nurses' Health Study II. We assayed estradiol, progesterone, prolactin, sex hormone binding globulin (SHBG), insulin-like growth factor-I (IGF-I), and IGFBP-3 in 111 African American and 111 Asian American women, matched to 111 Caucasian women on age, day of luteal phase, and day, time, and fasting status at blood collection. We analyzed the association between race and hormone levels using robust linear regression methods. In multivariate models, compared with Caucasians, African Americans had 18% higher levels of estradiol (P < 0.01), 17% higher free estradiol (P < 0.01), 11% lower SHBG (P = 0.05), 11% higher IGF-I (P < 0.01), 25% higher free IGF-I (P < 0.01), and 9% lower IGFBP-3 (P < 0.01) levels. In multivariate models, compared with Caucasian women, Asian Americans had 22% higher calculated free estradiol (P < 0.01), 31% lower SHBG (P < 0.01), and 25% higher free IGF-I (P < 0.01) levels. No racial differences were found in progesterone and prolactin levels. Our study showed hormone differences consistent with breast cancer risk between Caucasians and African Americans but inconsistent with breast cancer risk between Asian Americans and Caucasians. Further research is needed to explore differences across racial groups and the link between endogenous hormones and breast cancer risk.

A software program based on robust linear regression methods for instrumental calibration in biochemical analysis

A microcomputer program written in GWBASIC for conventional least squares regression (LS) and robust linear regression methods (RRMs) such as single median (SM) and repeated median (RM) is described. The main advantages of RRMs is the ability to detect outliers which can cause an inaccurate estimation of the analyzed samples. It requires MS DOS PC version 3.3 or higher and at least 256 kbyte of RAM. The joint application of RRMs and residuals analysis by the studentized method (STRM) allows a more precise biochemical analysis.