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By
Qin, Guoyou; Zhu, Zhongyi; Fung, Wing K.
3 Citations
In this paper, we study the robust estimation of generalized partially linear models (GPLMs) for longitudinal data with dropouts. We aim at achieving robustness against outliers. To this end, a weighted likelihood method is first proposed to obtain the robust estimation of the parameters involved in the dropout model for describing the missing process. Then, a robust inverse probabilityweighted generalized estimating equation is developed to achieve robust estimation of the mean model. To approximate the nonparametric function in the GPLM, a regression spline smoothing method is adopted which can linearize the nonparametric function such that statistical inference can be conducted operationally as if a generalized linear model was used. The asymptotic properties of the proposed estimator are established under some regularity conditions, and simulation studies show the robustness of the proposed estimator. In the end, the proposed method is applied to analyze a real data set.
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By
Yamada, Eika
In this study, we derive the asymptotic normality of a class of rank estimators in a simple spatial linear regression model, when errors form a strongly mixing random field and when the spatial data are both on the lattice and on the irregularly spaced spatial sites. This result in turn is used to investigate the asymptotic relative efficiency (ARE) of these estimators relative to the LSE. In addition, we conduct numerical experiments under both the lattice and the irregularly spaced sampling, which lends support to the robustness of these estimators compared to the LSE.
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By
Galea, Manuel; Paula, Gilberto A.; UribeOpazo, Miguel
31 Citations
We discuss in this paper the assessment of local influence in univariate elliptical linear regression models. This class includes all symmetric continuous distributions, such as normal, Studentt, Pearson VII, exponential power and logistic, among others. We derive the appropriate matrices for assessing the local influence on the parameter estimates and on predictions by considering as influence measures the likelihood displacement and a distance based on the Pearson residual. Two examples with real data are given for illustration.
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By
Mbah, Chamberlain; Peremans, Kris; Van Aelst, Stefan; Benoit, Dries F.
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A robust Bayesian model for seemingly unrelated regression is proposed. By using heavytailed distributions for the likelihood, robustness in the response variable is attained. In addition, this robust procedure is combined with a diagnostic approach to identify observations that are far from the bulk of the data in the multivariate space spanned by all variables. The most distant observations are downweighted to reduce the effect of leverage points. The resulting robust Bayesian model can be interpreted as a heteroscedastic seemingly unrelated regression model. Robust Bayesian estimates are obtained by a Markov Chain Monte Carlo approach. Complications by using a heavytailed error distribution are resolved efficiently by representing these distributions as a scale mixture of normal distributions. Monte Carlo simulation experiments confirm that the proposed model outperforms its traditional Bayesian counterpart when the data are contaminated in the response and/or the input variables. The method is demonstrated on a real dataset.
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By
GarcíaPérez, A.
In this paper, we obtain a saddlepoint approximation for the small sample distribution of several variogram estimators such as the classical Matheron’s estimator, some Mestimators like the robust Huber’s variogram estimator, and also the
$$\alpha $$
trimmed variogram estimator. The tail probability approximation obtained is very accurate even for small sample sizes. In the approximations we consider that the observations follow a distribution close to the normal, specifically, a scale contaminated normal model. To obtain the approximations we transform the original observations into a new ones, which can be considered independent if a linearized variogram can be accepted as model for them. To check this, a goodness of fit test for a variogram model is defined in the last part of the paper.
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By
Branco, J. A.; Croux, C.; Filzmoser, P.; Oliveira, M. R.
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30 Citations
Summary
Several approaches for robust canonical correlation analysis will be presented and discussed. A first method is based on the definition of canonical correlation analysis as looking for linear combinations of two sets of variables having maximal (robust) correlation. A second method is based on alternating robust regressions. These methods are discussed in detail and compared with the more traditional approach to robust canonical correlation via covariance matrix estimates. A simulation study compares the performance of the different estimators under several kinds of sampling schemes. Robustness is studied as well by breakdown plots.
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By
Zuo, Yijun
Depth notions in regression have been systematically proposed and examined in Zuo (
arXiv:1805.02046
, 2018). One of the prominent advantages of the notion of depth is that it can be directly utilized to introduce mediantype deepest estimating functionals (or estimators in the case of empirical distributions) for location or regression parameters in a multidimensional setting. Regression depth shares the advantage. Depth induced deepest estimating functionals are expected to inherit desirable and inherent robustness properties (e.g. bounded maximum bias and influence function and high breakdown point) as their univariate location counterpart does. Investigating and verifying the robustness of the deepest projection estimating functional (in terms of maximum bias, asymptotic and finite sample breakdown point, and influence function) is the major goal of this article. It turns out that the deepest projection estimating functional possesses a bounded influence function and the best possible asymptotic breakdown point as well as the best finite sample breakdown point with robust choice of its univariate regression and scale component.
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By
de la Rosa de Sáa, Sara; Lubiano, María Asunción; Sinova, Beatriz; Filzmoser, Peter
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4 Citations
Observations distant from the majority or deviating from the general pattern often appear in datasets. Classical estimates such as the sample mean or the sample variance can be substantially affected by these observations (outliers). Even a single outlier can have huge distorting influence. However, when one deals with realvalued data there exist robust measures/estimates of location and scale (dispersion) which reduce the influence of these atypical values and provide approximately the same results as the classical estimates applied to the typical data without outliers. In reallife, data to be analyzed and interpreted are not always precisely defined and they cannot be properly expressed by using a numerical scale of measurement. Frequently, some of these imprecise data could be suitably described and modelled by considering a fuzzy rating scale of measurement. In this paper, several wellknown scale (dispersion) estimators in the realvalued case are extended for random fuzzy numbers (i.e., random mechanisms generating fuzzyvalued data), and some of their properties as estimators for dispersion are examined. Furthermore, their robust behaviour is analyzed using two powerful tools, namely, the finite sample breakdown point and the sensitivity curves. Simulations, including empirical bias curves, are performed to complete the study.
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By
Zang, Yangguang; Zhao, Yinjun; Zhang, Qingzhao; Chai, Hao; Zhang, Sanguo; Ma, Shuangge
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For complex diseases, the interactions between genetic and environmental risk factors can have important implications beyond the main effects. Many of the existing interaction analyses conduct marginal analysis and cannot accommodate the joint effects of multiple main effects and interactions. In this study, we conduct joint analysis which can simultaneously accommodate a large number of effects. Significantly different from the existing studies, we adopt loss functions based on relative errors, which offer a useful alternative to the “classic” methods such as the least squares and least absolute deviation. Further to accommodate censoring in the response variable, we adopt a weighted approach. Penalization is used for identification and regularized estimation. Computationally, we develop an effective algorithm which combines the majorizeminimization and coordinate descent. Simulation shows that the proposed approach has satisfactory performance. We also analyze lung cancer prognosis data with gene expression measurements.
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By
Turkmen, Asuman; Billor, Nedret
2 Citations
Classification of samples into two or multiclasses is to interest of scientists in almost every field. Traditional statistical methodology for classification does not work well when there are more variables (p) than there are samples (n) and it is highly sensitive to outlying observations. In this study, a robust partial least squares based classification method is proposed to handle data containing outliers where
$$n\ll p.$$
The proposed method is applied to wellknown benchmark datasets and its properties are explored by an extensive simulation study.
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