Michelli Barros

Influence diagnostics in log-Birnbaum-Saunders regression models with censored data

In this paper we discuss log-Birnbaum-Saunders regression models with censored observations. This kind of model has been largely applied to study material lifetime subject to failure or stress. The score functions and observed Fisher information matrix are given as well as the process for estimating the regression coefficients and shape parameter is discussed. The normal curvatures of local influence are derived under various perturbation schemes and two deviance-type residuals are proposed to assess departures from the log-Birnbaum-Saunders error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed under log-Birnbaum-Saunders regression models. A diagnostic analysis is performed in order to select an appropriate model.

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

An R implementation for generalized Birnbaum-Saunders distributions

The Birnbaum-Saunders (BS) model is a positively skewed statistical distribution that has received great attention in recent decades. A generalized version of this model was derived based on symmetrical distributions in the real line named the generalized BS (GBS) distribution. The R package named gbs was developed to analyze data from GBS models. This package contains probabilistic and reliability indicators and random number generators from GBS distributions. Parameter estimates for censored and uncensored data can also be obtained by means of likelihood methods from the gbs package. Goodness-of-fit and diagnostic methods were also implemented in this package in order to check the suitability of the GBS models. In this article, the capabilities and features of the gbs package are illustrated by using simulated and real data sets. Shape and reliability analyses for GBS models are presented. A simulation study for evaluating the quality and sensitivity of the estimation method developed in the package is provided and discussed.

Birnbaum–Saunders statistical modelling: a new approach

Modelling based on the Birnbaum–Saunders distribution has received considerable attention in recent years. In this article, we introduce a new approach for Birnbaum–Saunders regression models, which allows us to analyze data in their original scale and to model non-constant variance. In addition, we propose four types of residuals for these models and conduct a simulation study to establish which of them has a better performance. Moreover, we develop methods of local influence by calculating the normal curvatures under different perturbation schemes. Finally, we perform a statistical analysis with real data by using the approach proposed in the article. This analysis shows the potentiality of our proposal.

Goodness-of-Fit Tests for the Birnbaum-Saunders Distribution With Censored Reliability Data

We propose goodness-of-fit tests for Birnbaum-Saunders distributions with type-II right censored data. Classical goodness-of-fit tests based on the empirical distribution, such as Anderson-Darling, Cramér-von Misses, and Kolmogorov-Smirnov, are adapted to censored data, and evaluated by means of a simulation study. The obtained results are applied to real-world censored reliability data.

Influence diagnostics in the tobit censored response model

In this article, we develop influence diagnostic tools for the tobit model. Specifically, we discuss global influence methods based on the Cook distance and residuals with envelopes, and total and conformal local influence techniques. In order to analyze the sensitivity of the maximum likelihood estimators of the parameters of the model to small perturbations on the assumptions of the model and/or data, we consider several perturbation schemes, such as case-weight and response perturbations. Finally, we illustrate the developed methodology by means of a real data set.

Generalized Tobit models: diagnostics and application in econometrics

ABSTRACT The standard Tobit model is constructed under the assumption of a normal distribution and has been widely applied in econometrics. Atypical/extreme data have a harmful effect on the maximum likelihood estimates of the standard Tobit model parameters. Then, we need to count with diagnostic tools to evaluate the effect of extreme data. If they are detected, we must have available a Tobit model that is robust to this type of data. The family of elliptically contoured distributions has the Laplace, logistic, normal and Student-t cases as some of its members. This family has been largely used for providing generalizations of models based on the normal distribution, with excellent practical results. In particular, because the Student-t distribution has an additional parameter, we can adjust the kurtosis of the data, providing robust estimates against extreme data. We propose a methodology based on a generalization of the standard Tobit model with errors following elliptical distributions. Diagnostics in the Tobit model with elliptical errors are developed. We derive residuals and global/local influence methods considering several perturbation schemes. This is important because different diagnostic methods can detect different atypical data. We implement the proposed methodology in an R package. We illustrate the methodology with real-world econometrical data by using the R package, which shows its potential applications. The Tobit model based on the Student-t distribution with a small quantity of degrees of freedom displays an excellent performance reducing the influence of extreme cases in the maximum likelihood estimates in the application presented. It provides new empirical evidence on the capabilities of the Student-t distribution for accommodation of atypical data.

Hypothesis testing in the unrestricted and restricted parametric spaces of structural models

Hypothesis for testing the equality of slopes in measurement error models, incorporating the additional assumption that the slopes lie in a closed interval is considered. Wald type statistics based on the maximum likelihood estimators are considered under both, restricted and unrestricted parametric spaces. Their asymptotic behaviors are analyzed through different simulation studies. The statistics performance is analyzed in terms of power. Analysis of the results suggests that the statistics considered under the restricted parametric space has shown a better performance since the tests based on these statistics are more powerful. An example illustrates the proposal.