2,392 research outputs found

    Significance Regression: Robust Regression for Collinear Data

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    This paper examines robust linear multivariable regression from collinear data. A brief review of M-estimators discusses the strengths of this approach for tolerating outliers and/or perturbations in the error distributions. The review reveals that M-estimation may be unreliable if the data exhibit collinearity. Next, significance regression (SR) is discussed. SR is a successful method for treating collinearity but is not robust. A new significance regression algorithm for the weighted-least-squares error criterion (SR-WLS) is developed. Using the weights computed via M-estimation with the SR-WLS algorithm yields an effective method that robustly mollifies collinearity problems. Numerical examples illustrate the main points

    Regression analysis of simulation experiments: Functional software specification

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    Computer Science;Operational Research

    Least absolute deviation estimation of linear econometric models: A literature review

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    Econometricians generally take for granted that the error terms in the econometric models are generated by distributions having a finite variance. However, since the time of Pareto the existence of error distributions with infinite variance is known. Works of many econometricians, namely, Meyer & Glauber (1964), Fama (1965) and Mandlebroth (1967), on economic data series like prices in financial and commodity markets confirm that infinite variance distributions exist abundantly. The distribution of firms by size, behaviour of speculative prices and various other recent economic phenomena also display similar trends. Further, econometricians generally assume that the disturbance term, which is an influence of innumerably many factors not accounted for in the model, approaches normality according to the Central Limit Theorem. But Bartels (1977) is of the opinion that there are limit theorems, which are just likely to be relevant when considering the sum of number of components in a regression disturbance that leads to non-normal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a non-normal distribution exists. The Least Squares method of estimation of parameters of linear (regression) models performs well provided that the residuals (disturbances or errors) are well behaved (preferably normally or near-normally distributed and not infested with large size outliers) and follow Gauss-Markov assumptions. However, models with the disturbances that are prominently non-normally distributed and contain sizeable outliers fail estimation by the Least Squares method. An intensive research has established that in such cases estimation by the Least Absolute Deviation (LAD) method performs well. This paper is an attempt to survey the literature on LAD estimation of single as well as multi-equation linear econometric models.Lad estimator; Least absolute deviation estimation; econometric model; LAD Estimator; Minimum Absolute Deviation; Robust; Outliers; L1 Estimator; Review of literature

    Robust Estimation for Linear Panel Data Models

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    In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making meaningful statistical inferences. However, when the ordinary least squares (OLS) method is used to estimate the model parameters, presence of outliers may significantly alter the adequacy of such models by producing biased and inefficient estimates. In this work we propose a new, weighted likelihood based robust estimation procedure for linear panel data models with fixed and random effects. The finite sample performances of the proposed estimators have been illustrated through an extensive simulation study as well as with an application to blood pressure data set. Our thorough study demonstrates that the proposed estimators show significantly better performances over the traditional methods in the presence of outliers and produce competitive results to the OLS based estimates when no outliers are present in the data set

    Aspects of estimation in the linear model with special reference to collinearity

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    The L-sigma Relation of Local HII Galaxies

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    We present for the first time a new data set of emission line widths for 118 star-forming regions in HII galaxies (HIIGs). This homogeneous set is used to investigate the L-sigma relation in conjunction with optical spectrophotometric observations. Peculiarities in the line profiles such as sharp lines, wings, asymmetries, and in some cases more than one component in emission were verified. From a new independent homogeneous set of spectrophotometric data we derived physical condition parameters and performed the statistical principal component analysis. We have investigated the potential role of metallicity (O/H), Hbeta equivalent width (WHbeta) and ionization ratio [OIII]/[OII] to account for the observational scatter of L-sigma relation. Our results indicate that the L-sigma relation for HIIGs is more sensitive to the evolution of the current starburst event (short-term evolution) and dated by WHbeta or even the [OIII]/[OII] ratio. The long-term evolution measured by O/H also plays a potential role in determining the luminosity of the current burst for a given velocity dispersion and age as previously suggested. Additionally, galaxies showing Gaussian line profiles present more tight correlations indicating that they are best targets for the application of the parametric relations as an extragalactic cosmological distance indicator. Best fits for a restricted homogeneous sample of 45 HIIGs provide us a set of new extragalactic distance indicators with an RMS scatter compatible with observational errors of Delta_log(LHalpha) = 0.2 dex or 0.5 mag. Improvements may still come from future optimized observational programs to reduce the observational uncertainties on the predicted luminosities of HIIGs in order to achieve the precision required for the application of these relations as tests of cosmological models.Comment: 53 pages, 15 figures, 4 complete tables Accepted for publication in The Astrophysical Journa

    Collinearity and consequences for estimation: a study and simulation

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    Data Health Assurance in Social and Behavioral Sciences Research

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    This illustrative study reincarnates the philosophical assumption of Methodology for science among other assumptions like Epistemology and Ontology in the context of social and behavioral sciences. Based on literature review the study divided the overlapping and perplexing Gaussian Linear Regression Model (GLRM) assumptions into two comprehensive groups. The study modeled straightforward diagnostics for GLRM assumptions violations by using the data collected from 150 postgraduate university students. Finally, the study provides the remedial directions to address possible problems created by GLRM assumptions violations
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