arXiv subjects

Silvia L. P. Ferrari

Publications and source records attributed to Silvia L. P. Ferrari.

At least 19 recordsLinked to original sources

arXiv2022

Robust beta regression through the logit transformation

Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural sciences. The maximum likelihood estimation is widely used to make inferences for the parameters. Nonetheless, it is well-known that the maximum likelihood-based inference suffers from the lack of robustness in the presence of outliers. Such a case can bring severe bias and misleading conclusions. Recently, robust estimators for beta regression models were presented in the literature. However, these estimators require non-trivial restrictions in the parameter space, which limit their application. This paper develops new robust estimators that overcome this drawback. Their asymptotic and robustness properties are studied, and robust Wald-type tests are introduced. Simulation results evidence the merits of the new robust estimators. Inference and diagnostics using the new estimators are illustrated in an application to health insurance coverage data.

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arXiv2022

Robust estimation in beta regression via maximum Lq-likelihood

Beta regression models are widely used for modeling continuous data limited to the unit interval, such as proportions, fractions, and rates. The inference for the parameters of beta regression models is commonly based on maximum likelihood estimation. However, it is known to be sensitive to discrepant observations. In some cases, one atypical data point can lead to severe bias and erroneous conclusions about the features of interest. In this work, we develop a robust estimation procedure for beta regression models based on the maximization of a reparameterized Lq-likelihood. The new estimator offers a trade-off between robustness and efficiency through a tuning constant. To select the optimal value of the tuning constant, we propose a data-driven method which ensures full efficiency in the absence of outliers. We also improve on an alternative robust estimator by applying our data-driven method to select its optimum tuning constant. Monte Carlo simulations suggest marked robustness of the two robust estimators with little loss of efficiency. Applications to three datasets are presented and discussed. As a by-product of the proposed methodology, residual diagnostic plots based on robust fits highlight outliers that would be masked under maximum likelihood estimation.

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arXiv2020

Higher-order approximate confidence intervals

Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence intervals based on higher-order approximate quantiles of the score function. The coverage approximation error is $O(n^{-3/2})$ while the approximation error of confidence intervals based on the asymptotic normality of MLEs is $O(n^{-1/2})$. Monte Carlo simulations confirm the theoretical findings. An implementation for regression models and real data applications are provided.

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arXiv2017

Box-Cox elliptical distributions with application

We propose and study the class of Box-Cox elliptical distributions. It provides alternative distributions for modeling multivariate positive, marginally skewed and possibly heavy-tailed data. This new class of distributions has as a special case the class of log-elliptical distributions, and reduces to the Box-Cox symmetric class of distributions in the univariate setting. The parameters are interpretable in terms of quantiles and relative dispersions of the marginal distributions and of associations between pairs of variables. The relation between the scale parameters and quantiles makes the Box-Cox elliptical distributions attractive for regression modeling purposes. Applications to data on vitamin intake are presented and discussed.

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arXiv2017

Box-Cox symmetric distributions and applications to nutritional data

We introduce the Box-Cox symmetric class of distributions, which is useful for modeling positively skewed, possibly heavy-tailed, data. The new class of distributions includes the Box-Cox t, Box-Cox Cole-Gree, Box-Cox power exponential distributions, and the class of the log-symmetric distributions as special cases. It provides easy parameter interpretation, which makes it convenient for regression modeling purposes. Additionally, it provides enough flexibility to handle outliers. The usefulness of the Box-Cox symmetric models is illustrated in applications to nutritional data.

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arXiv2016

Small-sample testing inference in symmetric and log-symmetric linear regression models

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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arXiv2016

Improved estimation in a general multivariate elliptical model

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in common. Many frequently used models are special cases of this general formulation, namely: errors-in-variables models, nonlinear mixed-effects models, heteroscedastic nonlinear models, among others. In any of these models, the vector of the errors may have any multivariate elliptical distribution. We obtain the second-order bias of the maximum likelihood estimator, a bias-corrected estimator, and a bias-reduced estimator. Simulation results indicate the effectiveness of the bias correction and bias reduction schemes.

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arXiv2014

A class of regression models for parallel and series systems with a random number of components

In this paper we extend the Weibull power series (WPS) class of distributions and named this new class as extended Weibull power series (EWPS) class of distributions. The EWPS distributions are related to series and parallel systems with a random num- ber of components, whereas the WPS distributions (Morais and Barreto-Souza, 2011) are related to series systems only. Unlike the WPS distributions, for which the Weibull is a limiting special case, the Weibull law is a particular case of the EWPS distributions. We prove that the distributions in this class are identifiable under a simple assumption. We also prove stochastic and hazard rate order results and highlight that the shapes of the EWPS distributions are markedly more flexible than the shapes of the WPS distributions. We define a regression model for the EWPS response random variable to model a scale parameter and its quantiles. We present the maximum likelihood estimator and prove its consistency and normal asymptotic distribution. Although the construction of this class was motivated by series and parallel systems, the EWPS distributions are suitable for modeling a wide range of positive data sets. To illustrate potential uses of this model, we apply it to a real data set on the tensile strength of coconut fibers and present a simple device for diagnostic purposes.

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arXiv2014

Small-sample one-sided testing in extreme value regression models

We derive adjusted signed likelihood ratio statistics for a general class of extreme value regression models. The adjustments reduce the error in the standard normal approximation to the distribution of the signed likelihood ratio statistic. We use Monte Carlo simulations to compare the finite-sample performance of the different tests. Our simulations suggest that the signed likelihood ratio test tends to be liberal when the sample size is not large, and that the adjustments are effective in shrinking the size distortion. Two real data applications are presented and discussed.

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arXiv2013

Improved likelihood inference in generalized linear models

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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arXiv2013

Errors-in-variables beta regression models

Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0,1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error. The structural approach, in which the covariates measured with error are assumed to be random variables, is employed. Three estimation methods are presented, namely maximum likelihood, maximum pseudo-likelihood and regression calibration. Monte Carlo simulations are used to evaluate the performance of the proposed estimators and the naïve estimator. Also, a residual analysis for beta regression models with measurement errors is proposed. The results are illustrated in a real data set.

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arXiv2013

Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of distributions, which has the normal distribution as a special case. We derive the Skovgaard adjusted likelihood ratio statistics, which follow a chi-squared distribution with a high degree of accuracy. We conduct a simulation study and show that the proposed tests display superior finite sample behavior as compared to the standard likelihood ratio test. We illustrate the usefulness of our results in applied settings using a data set from the WHO MONICA Projection cardiovascular disease.

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arXiv2012

Mixed Beta Regression: A Bayesian Perspective

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian approach. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter, and allow both parameters to be modeled through regression structures that may involve fixed and random effects. Specification of prior distributions is discussed, computational implementation via Gibbs sampling is provided, and illustrative examples are presented.

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arXiv2012

Small-sample likelihood inference in extreme-value regression models

We deal with a general class of extreme-value regression models introduced by Barreto- Souza and Vasconcellos (2011). Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as \c{hi}2 with a high degree of accuracy. Although the adjusted statistic requires more computational effort than its unadjusted counterpart, it is shown that the adjustment term has a simple compact form that can be easily implemented in standard statistical software. Further, we compare the finite sample performance of the three classical tests (likelihood ratio, Wald, and score), the gradient test that has been recently proposed by Terrell (2002), and the adjusted likelihood ratio test obtained in this paper. Our simulations favor the latter. Applications of our results are presented. Key words: Extreme-value regression; Gradient test; Gumbel distribution; Likelihood ratio test; Nonlinear models; Score test; Small-sample adjustments; Wald test.

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arXiv2012

Gradient statistic: higher-order asymptotics and Bartlett-type correction

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.

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arXiv2011

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented.

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arXiv2011

Adjusted likelihood inference in an elliptical multivariate errors-in-variables model

In this paper we obtain an adjusted version of the likelihood ratio test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as a special case. We derive a modified likelihood ratio statistic that follows a chi-squared distribution with a high degree of accuracy. Our results generalize those in Melo and Ferrari(Advances in Statistical Analysis, 2010, 94, 75-87) by allowing the parameter of interest to be vector-valued in the multivariate errors-in-variables model. We report a simulation study which shows that the proposed test displays superior finite sample behavior relative to the standard likelihood ratio test.

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arXiv2011

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Oftentimes, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test and also to a test obtained from a modified profile likelihood function. Our results generalize those in Zucker et al. (Journal of the Royal Statistical Society B, 2000, 62, 827-838) by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report numerical evidence which shows that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed.

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