92 research outputs found
The minimum S-divergence estimator under continuous models: the Basu–Lindsay approach
No full textRobust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (A Generalized Divergence for Statistical Inference, 2013a) proposed a general class of divergence measures for robust statistical inference, named the S-divergence family. Ghosh (Sankhya A, doi:10.1007/s13171-014-0063-2, 2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the minimum S-divergence estimators under continuous models. Here we use the Basu–Lindsay approach (Ann Inst Stat Math 46:683–705, 1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples
The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach
No full textRobust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures for robust statistical inference, named the S-Divergence Family. Ghosh (2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under continuous models. Here we use the Basu-Lindsay approach (1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples.
Minimum disparity estimation in the errors-in-variables model
No full textRobust estimators are determined using the minimum disparity estimation method (Lindsay, 1994; Basu and Lindsay, 1994) in the errors-in-variables model. These estimators are asymptotically fully efficient for the model considered and have strong robustness features. In a numerical example these estimators compare favorably with the orthogonal regression M-estimators of Zamar (1989).Hellinger distance Kernel density estimation Robustness Transparent kernel
A Robust Wald-Type Test for Testing the Equality of Two Means from Log-Normal Samples
No full textThe log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis for comparing the means of two independent log-normal distributions is an issue of significant interest. In this paper we present a robust test for this problem. The unknown parameters of the model are estimated by minimum density power divergence estimators (Basu et al. Biometrika 85(3):549–559 1998). The robustness as well as the asymptotic properties of the proposed test statistics are rigorously established. The performance of the test is explored through simulations and real data analysis. The test is compared with some existing methods, and it is demonstrated that the proposed test outperforms the others in the presence of outliers
A New Class of Robust Two-Sample Wald-Type Tests
No full textParametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameters. In particular, we consider the simple two-sample hypothesis concerning the full parametric homogeneity as well as the general two-sample (composite) hypotheses involving some nuisance parameters. The asymptotic and theoretical robustness properties of the proposed Wald-type tests have been developed for both the simple and general composite hypotheses. Some particular cases of testing against one-sided alternatives are discussed with specific attention to testing the effectiveness of a treatment in clinical trials. Performances of the proposed tests have also been illustrated numerically through appropriate real data examples.Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasTRUEpu
Comparison of several goodness‐of‐fit tests for the kappa statistic based on exact power and coverage probability
No full textRobust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach
No full text<div><p>The density power divergence (DPD) measure, defined in terms of a single parameter <i>α</i>, has proved to be a popular tool in the area of robust estimation [<a href="#CIT0001" target="_blank">1</a>]. Recently, Ghosh and Basu [<a href="#CIT0005" target="_blank">5</a>] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observations. In this paper, we present an extensive numerical study to describe the performance of the method in the case of linear regression, the most common setup under the case of non-homogeneous data. In addition, we extend the existing methods for the selection of the optimal robustness tuning parameter from the case of independent and identically distributed (i.i.d.) data to the case of non-homogeneous observations. Proper selection of the tuning parameter is critical to the appropriateness of the resulting analysis. The selection of the optimal robustness tuning parameter is explored in the context of the linear regression problem with an extensive numerical study involving real and simulated data.</p></div
Robust estimation of fixed effect parameters and variances of linear mixed models: the minimum density power divergence approach
No full textMany real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non-identically distributed observations for LMMs according to the variance components model. We prove that the theoretical properties hold, including consistency and asymptotic normality of the estimators. The influence function and sensitivity measures are computed to explore the robustness properties. As a data-based choice of the MDPDE tuning parameter α is very important, we propose two candidates as “optimal” choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of α, with S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example
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