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Basu Ayanendranath Ghosh Abhik Mandal Abhijit Martin Nirian Pardo Leandro 《Statistical Methods and Applications》2021,30(3):973-1005
Statistical Methods & Applications - We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum... 相似文献
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It sometimes occurs that one or more components of the data exert a disproportionate influence on the model estimation. We need a reliable tool for identifying such troublesome cases in order to decide either eliminate from the sample, when the data collect was badly realized, or otherwise take care on the use of the model because the results could be affected by such components. Since a measure for detecting influential cases in linear regression setting was proposed by Cook [Detection of influential observations in linear regression, Technometrics 19 (1977), pp. 15–18.], apart from the same measure for other models, several new measures have been suggested as single-case diagnostics. For most of them some cutoff values have been recommended (see [D.A. Belsley, E. Kuh, and R.E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, 2nd ed., John Wiley & Sons, New York, Chichester, Brisban, (2004).], for instance), however the lack of a quantile type cutoff for Cook's statistics has induced the analyst to deal only with index plots as worthy diagnostic tools. Focussed on logistic regression, the aim of this paper is to provide the asymptotic distribution of Cook's distance in order to look for a meaningful cutoff point for detecting influential and leverage observations. 相似文献
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For some discrete state series, such as DNA sequences, it can often be postulated that its probabilistic behaviour is given by a Markov chain. For making the decision on whether or not an uncharacterized piece of DNA is part of the coding region of a gene, under the Markovian assumption, there are two statistical tools that are essential to be considered: the hypothesis testing of the order in a Markov chain and the estimators of transition probabilities. In order to improve the traditional statistical procedures for both of them when stationarity assumption can be considered, a new version for understanding the homogeneity hypothesis is proposed so that log-linear modelling is applied for conditional independence jointly with homogeneity restrictions on the expected means of transition counts in the sequence. In addition we can consider a variety of test-statistics and estimators by using φ-divergence measures. As special case of them the well-known likelihood ratio test-statistics and maximum-likelihood estimators are obtained. 相似文献
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Apostolos Batsidis Nirian Martin Leandro Pardo Konstantinos Zografos 《统计学通讯:模拟与计算》2013,42(10):2253-2271
In a recent article, Cardoso de Oliveira and Ferreira have proposed a multivariate extension of the univariate chi-squared normality test, using a known result for the distribution of quadratic forms in normal variables. In this article, we propose a family of power divergence type test statistics for testing the hypothesis of multinormality. The proposed family of test statistics includes as a particular case the test proposed by Cardoso de Oliveira and Ferreira. We assess the performance of the new family of test statistics by using Monte Carlo simulation. In this context, the type I error rates and the power of the tests are studied, for important family members. Moreover, the performance of significant members of the proposed test statistics are compared with the respective performance of a multivariate normality test, proposed recently by Batsidis and Zografos. Finally, two well-known data sets are used to illustrate the method developed in this article as well as the specialized test of multivariate normality proposed by Batsidis and Zografos. 相似文献
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Tomáš Hobza Nirian Martín Leandro Pardo 《Journal of Statistical Computation and Simulation》2017,87(12):2309-2333
In this paper a new robust estimator, modified median estimator, is introduced and studied for the logistic regression model. This estimator is based on the median estimator considered in Hobza et al. [Robust median estimator in logistic regression. J Stat Plan Inference. 2008;138:3822–3840]. Its asymptotic distribution is obtained. Using the modified median estimator, we also consider a Wald-type test statistic for testing linear hypotheses in the logistic regression model and we obtain its asymptotic distribution under the assumption of random regressors. An extensive simulation study is presented in order to analyse the efficiency as well as the robustness of the modified median estimator and Wald-type test based on it. 相似文献
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We consider the asymptotic distribution of divergence-based influence measures which are an extension for polytomous logistic regression of an influence measure proposed in Johnson (1985), for binary logistic regression. A numerical example compares the classical Cook’s distance with the divergence based influence measures. 相似文献
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Elena Castilla Nirian Martín Leandro Pardo 《AStA Advances in Statistical Analysis》2018,102(3):381-411
This article develops the theoretical framework needed to study the multinomial regression model for complex sample design with pseudo-minimum phi-divergence estimators. The numerical example and the simulation study propose new estimators for the parameter of the logistic regression with overdispersed multinomial distributions for the response variables, the pseudo-minimum Cressie–Read divergence estimators, as well as new estimators for the intra-cluster correlation coefficient. The simulation study shows that the Binder’s method for the intra-cluster correlation coefficient exhibits an excellent performance when the pseudo-minimum Cressie–Read divergence estimator, with \(\lambda =\frac{2}{3}\), is plugged. 相似文献
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