The Experts below are selected from a list of 87 Experts worldwide ranked by ideXlab platform
Artur J Lemonte - One of the best experts on this subject based on the ideXlab platform.
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Likelihood-based tests in zero-inflated power series models
Journal of Statistical Computation and Simulation, 2018Co-Authors: Katherine E. C. Zavaleta, Vicente G. Cancho, Artur J LemonteAbstract:ABSTRACTWe address the issue of performing testing inference in the class of zero-inflated power series models. These models provide a straightforward way of modelling count data and have been widely used in practical situations. The likelihood ratio, Wald and score Statistics provide the basis for testing the parameter of inflation of zeros in this class of models. In this paper, in addition to the well-known test Statistics, we also consider the recently proposed Gradient Statistic. We conduct Monte Carlo simulation experiments to evaluate the finite-sample performance of these tests for testing the parameter of inflation of zeros. The numerical results show that the new Gradient test we propose is more reliable in finite samples than the usual likelihood ratio, Wald and score tests. An empirical application to real data is considered for illustrative purposes.
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Improved inference in dispersion models
Applied Mathematical Modelling, 2017Co-Authors: Francisco Medeiros, Silvia L P Ferrari, Artur J LemonteAbstract:Abstract We derive a general matrix Bartlett–type correction factor to the Gradient Statistic in the class of dispersion models. The correction improves the large–sample χ 2 approximation to the null distribution of the Gradient Statistic when the sample size is finite. We conduct Monte Carlo simulation experiments to evaluate and compare the performance of various different tests, namely the usual Wald, likelihood ratio, score, and Gradient tests, the Bartlett–corrected versions of the likelihood ratio, score, and Gradient tests, and bootstrap–based tests. The simulation results suggest that the analytical and computational corrections are effective in removing size distortions of the type I error probability with no power loss. The impact of the corrections in two real data applications is considered for illustrative purposes.
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the Gradient Statistic
The Gradient Test#R##N#Another Likelihood-Based Test, 2016Co-Authors: Artur J LemonteAbstract:In this chapter, we introduce the new likelihood-based test Statistic named as the Gradient Statistic . The test that uses the Gradient Statistic is a newly large-sample test which was introduced in the Statistic literature by George R. Terrell. The Gradient Statistic is very simple to be computed and it can be an interesting alternative to the classical Statistics, namely the likelihood ratio, Wald, and Rao score Statistics. We provide some properties of the Gradient Statistic and present several examples.
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the bartlett corrected Gradient Statistic
The Gradient Test#R##N#Another Likelihood-Based Test, 2016Co-Authors: Artur J LemonteAbstract:In this chapter, the asymptotic expansion for the null distribution function of the Gradient Statistic for testing composite null hypotheses in the presence of nuisance parameters is presented. Using this expansion, a Bartlett-type corrected Gradient Statistic with χ 2 distribution up to an error of order O ( n −3/2 ) under the null hypothesis is constructed. Further, we also use the expansion to modify the percentage points of the large sample reference χ 2 distribution. We consider the Batlett-corrected Gradient Statistic in some parametric models and Monte Carlo simulations are presented and discussed.
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Improved likelihood inference in generalized linear models
Computational Statistics & Data Analysis, 2014Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical situations. The likelihood ratio, Wald and score Statistics, and the recently proposed Gradient Statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test Statistics. We derive a general Bartlett-type correction factor in matrix notation for the Gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and Gradient tests, and with the Bartlett-corrected likelihood ratio and score tests, and bootstrap-corrected tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.
Silvia L P Ferrari - One of the best experts on this subject based on the ideXlab platform.
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Improved inference in dispersion models
Applied Mathematical Modelling, 2017Co-Authors: Francisco Medeiros, Silvia L P Ferrari, Artur J LemonteAbstract:Abstract We derive a general matrix Bartlett–type correction factor to the Gradient Statistic in the class of dispersion models. The correction improves the large–sample χ 2 approximation to the null distribution of the Gradient Statistic when the sample size is finite. We conduct Monte Carlo simulation experiments to evaluate and compare the performance of various different tests, namely the usual Wald, likelihood ratio, score, and Gradient tests, the Bartlett–corrected versions of the likelihood ratio, score, and Gradient tests, and bootstrap–based tests. The simulation results suggest that the analytical and computational corrections are effective in removing size distortions of the type I error probability with no power loss. The impact of the corrections in two real data applications is considered for illustrative purposes.
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Small-sample testing inference in symmetric and log-symmetric linear regression models
arXiv: Methodology, 2016Co-Authors: Francisco Medeiros, Silvia L P FerrariAbstract:This paper deals with the issue of testing hypothesis in symmetric and log-symmetric linear regression models in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and Gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test Statistic and the corresponding chi-squared asymptotic distribution. Bartlett and Bartlett-type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in symmetric linear regression models. Here, we derive a Bartlett-type correction for the Gradient test. We show that the corrections are also valid for the log-symmetric linear regression models. We numerically compare the various tests, and bootstrapped tests, through simulations. Our results suggest that the corrected and bootstrapped tests exhibit type I probability error closer to the chosen nominal level with virtually no power loss. The analytically corrected tests, including the Bartlett-corrected Gradient test derived in this paper, perform as well as the bootstrapped tests with the advantage of not requiring computationally-intensive calculations. We present two real data applications to illustrate the usefulness of the modified tests. Keywords: Symmetric regression models; Bartlett correction; Bartlett-type correction; Bootstrap; Log-symmetric regression models; Gradient Statistic; score Statistic; likelihood ratio Statistic; Wald Statistic.
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Improved likelihood inference in generalized linear models
Computational Statistics & Data Analysis, 2014Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical situations. The likelihood ratio, Wald and score Statistics, and the recently proposed Gradient Statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test Statistics. We derive a general Bartlett-type correction factor in matrix notation for the Gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and Gradient tests, and with the Bartlett-corrected likelihood ratio and score tests, and bootstrap-corrected tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.
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Improved likelihood inference in generalized linear models
arXiv: Methodology, 2013Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical situations. The likelihood ratio, Wald and score Statistics, and the recently proposed Gradient Statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test Statistics. We derive a general Bartlett-type correction factor in matrix notation for the Gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and Gradient tests, and with the Bartlett-corrected likelihood ratio and score tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.
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Gradient Statistic higher order asymptotics and bartlett type correction
Electronic Journal of Statistics, 2013Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We obtain an asymptotic expansion for the null distribution function of the Gradient Statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the shrinkage argument described in [10]. Using this expansion, we propose a Bartlett-type corrected Gradient Statistic with chi-square distribution up to an error of order o(n) under the null hypothesis. Further, we also use the expansion to modify the percentage points of the large sample reference chi-square distribution. Monte Carlo simulation experiments and various examples are presented and discussed.
Tiago M Vargas - One of the best experts on this subject based on the ideXlab platform.
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Improved likelihood inference in generalized linear models
Computational Statistics & Data Analysis, 2014Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical situations. The likelihood ratio, Wald and score Statistics, and the recently proposed Gradient Statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test Statistics. We derive a general Bartlett-type correction factor in matrix notation for the Gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and Gradient tests, and with the Bartlett-corrected likelihood ratio and score tests, and bootstrap-corrected tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.
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Improved likelihood inference in generalized linear models
arXiv: Methodology, 2013Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical situations. The likelihood ratio, Wald and score Statistics, and the recently proposed Gradient Statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test Statistics. We derive a general Bartlett-type correction factor in matrix notation for the Gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and Gradient tests, and with the Bartlett-corrected likelihood ratio and score tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.
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Gradient Statistic higher order asymptotics and bartlett type correction
Electronic Journal of Statistics, 2013Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We obtain an asymptotic expansion for the null distribution function of the Gradient Statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the shrinkage argument described in [10]. Using this expansion, we propose a Bartlett-type corrected Gradient Statistic with chi-square distribution up to an error of order o(n) under the null hypothesis. Further, we also use the expansion to modify the percentage points of the large sample reference chi-square distribution. Monte Carlo simulation experiments and various examples are presented and discussed.
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Gradient Statistic higher order asymptotics and bartlett type correction
arXiv: Statistics Theory, 2012Co-Authors: Tiago M Vargas, Silvia L P Ferrari, Artur J LemonteAbstract:We obtain an asymptotic expansion for the null distribution function of theGradient Statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the shrinkage argument described in Ghosh and Mukerjee (1991). Using this expansion, we propose a Bartlett-type corrected Gradient Statistic with chi-square distribution up to an error of order o(n^{-1}) under the null hypothesis. Further, we also use the expansion to modify the percentage points of the large sample reference chi-square distribution. A small Monte Carlo experiment and various examples are presented and discussed.
Antonella Plaia - One of the best experts on this subject based on the ideXlab platform.
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A Gradient-based deletion diagnostic measure for generalized linear mixed models
Communications in Statistics-theory and Methods, 2016Co-Authors: Marco Enea, Antonella PlaiaAbstract:ABSTRACTA Gradient-Statistic-based diagnostic measure is developed in the context of the generalized linear mixed models. Its performance is assessed by some real examples and simulation studies, in terms of ability in detecting influential data structures and of concordance with the most used influence measures.
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Influence Diagnostics for Meta-Analysis of Individual Patient Data Using Generalized Linear Mixed Models
Studies in Classification Data Analysis and Knowledge Organization, 2014Co-Authors: Marco Enea, Antonella PlaiaAbstract:In meta-analysis, generalized linear mixed models (GLMMs) are usually used when heterogeneity is present and individual patient data (IPD) are available, while accepting binary, discrete as well as continuous response variables. In the present paper some measures of influence diagnostics based on log-likelihood are suggested and discussed. A known measure is approximated to get a simpler form, for which the information matrix is no more necessary. The performance of the proposed measure is assessed through a diagnostic analysis on simulated data reproducing a possible meta-analytical context of IPD with influential outliers. The proposed measure is showed to work well and to have a form similar to the Gradient Statistic, recently introduced.
Francisco Medeiros - One of the best experts on this subject based on the ideXlab platform.
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Improved inference in dispersion models
Applied Mathematical Modelling, 2017Co-Authors: Francisco Medeiros, Silvia L P Ferrari, Artur J LemonteAbstract:Abstract We derive a general matrix Bartlett–type correction factor to the Gradient Statistic in the class of dispersion models. The correction improves the large–sample χ 2 approximation to the null distribution of the Gradient Statistic when the sample size is finite. We conduct Monte Carlo simulation experiments to evaluate and compare the performance of various different tests, namely the usual Wald, likelihood ratio, score, and Gradient tests, the Bartlett–corrected versions of the likelihood ratio, score, and Gradient tests, and bootstrap–based tests. The simulation results suggest that the analytical and computational corrections are effective in removing size distortions of the type I error probability with no power loss. The impact of the corrections in two real data applications is considered for illustrative purposes.
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Small-sample testing inference in symmetric and log-symmetric linear regression models
arXiv: Methodology, 2016Co-Authors: Francisco Medeiros, Silvia L P FerrariAbstract:This paper deals with the issue of testing hypothesis in symmetric and log-symmetric linear regression models in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and Gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test Statistic and the corresponding chi-squared asymptotic distribution. Bartlett and Bartlett-type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in symmetric linear regression models. Here, we derive a Bartlett-type correction for the Gradient test. We show that the corrections are also valid for the log-symmetric linear regression models. We numerically compare the various tests, and bootstrapped tests, through simulations. Our results suggest that the corrected and bootstrapped tests exhibit type I probability error closer to the chosen nominal level with virtually no power loss. The analytically corrected tests, including the Bartlett-corrected Gradient test derived in this paper, perform as well as the bootstrapped tests with the advantage of not requiring computationally-intensive calculations. We present two real data applications to illustrate the usefulness of the modified tests. Keywords: Symmetric regression models; Bartlett correction; Bartlett-type correction; Bootstrap; Log-symmetric regression models; Gradient Statistic; score Statistic; likelihood ratio Statistic; Wald Statistic.
