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We consider a robust parametric procedure for estimating the structural parameters in functional measurement error models. The methodology extends the maximum Lq-likelihood approach to the more general problem of independent, but not identically distributed observations and the presence of incidental parameters. The proposal replaces the incidental parameters in the Lq-likelihood with their estimates, which depend on the structural parameter. The resulting estimator, called the maximum Lq-likelihood estimator (MLqE) adapts according to the discrepancy between the data and the postulated model by tuning a single parameter q, with 0 < q <1, that controls the trade-off between robustness and efficiency. The maximum likelihood estimator is obtained as a particular case when q = 1. We provide asymptotic properties of the MLqE under appropriate regularity conditions. Moreover, we describe the estimating algorithm based on a reweighting procedure, as well as a data-driven proposal for the choice of the tuning parameter q. The approach is illustrated and applied to the problem of estimating a bivariate linear normal relationship, including a small simulation study and an analysis of a real data set. [ABSTRACT FROM AUTHOR]

In this paper the influence measures for the Negative Binomial regression model are presented. Based on the conditional expectation of the complete-data log-likelihood function we derive some influence measures, such as case deletion (global influence) and local influence analysis. For the implementation of the influence measures we present explicit expressions and discuss an appropriate perturbation scheme. To illustrate the results, simulations and real data applications are presented. Results show that both global and local influence methods are effective in detecting possible observations that influence the parameter estimation, or at least in focusing researchers attention on those observations. [ABSTRACT FROM AUTHOR]

The Birnbaum‐Saunders (BS) distribution is a model that frequently appears in the statistical literature and has proved to be very versatile and efficient across a wide range of applications. However, despite the growing interest in the study of the BS distribution, quantile regression modeling has not been considered for this distribution. To fill this gap, we introduce a class of quantile regression models based on the BS distribution, which allows us to describe positive and asymmetric data when a quantile must be predicted using covariates. We use an approach based on a quantile parameterization to generate the model, permitting us to consider a similar framework to generalized linear models, providing wide flexibility. The methodology proposed includes a thorough study of theoretical properties and practical issues, such as maximum likelihood parameter estimation and diagnostic analytics based on local influence and residuals. The performance of the residuals is evaluated by simulations, whereas an illustrative example of income data is conducted using the methodology to show its potential for applications. The numerical results report an adequate performance of the approach to quantile regression, indicating that the BS distribution is a good modeling choice when dealing with data that have both positive support and asymmetry. The economic implications of our investigation are discussed in the final section. Hence, it can be a valuable addition to the tool kit of applied statisticians and econometricians. [ABSTRACT FROM AUTHOR]

In this paper, we consider a regression model under the generalized Waring distribution for modeling count data. We develop and implement local influence diagnostic techniques based on likelihood displacement. Also we develop case-deletion methods. The generalized Waring regression model is presented as a mixture of the Negative Binomial and the Beta II distributions, and it is compared to the Negative Binomial and Waring regression models. Estimation is performed by maximum likelihood function. The influence measures developed in this paper are applied to a Spanish football league data set. Empirical results show that the generalized Waring regression model performs better when compared to the Negative Binomial and Waring regression models. Technical details are presented in the Appendix. [ABSTRACT FROM AUTHOR]

A method is proposed in this paper to assess the local influence of minor perturbations for the Sharpe model when the normal distribution is replaced by normal/independent (NI) distributions. The family of NI distributions is an attractive class of symmetric heavy-tailed densities that includes as special cases the normal, t-Student, slash, and the contaminated normal distributions. Since the returns of the market are not observable, the statistical analysis is carried out in the context of an errors-in-variables model. An influence analysis for detecting influential observations (atypical returns) is developed to investigate the sensitivity of the maximum likelihood estimators. Diagnostic measures are obtained based on the conditional expectation of the complete-data log-likelihood function. The results are illustrated by using a set of shares of companies traded in the Chilean stock market. [ABSTRACT FROM AUTHOR]

In this paper we consider the capital asset pricing model under the multivariate normal distribution for modeling asset returns. We develop and implement local influence diagnostic techniques not based on likelihood displacement. The main interest is to consider the test of mean-variance efficiency of a given portfolio as objective function. Sensitivity of maximum likelihood estimators of slopes is also considered. For this purpose, first and second-order local influence measures are calculated under a case weights perturbation scheme. In particular, for our objective functions, which have nonzero first derivative at the critical point, the proposed second-order measures are scale invariant, unlike the normal curvature. The performance of the proposed measures is illustrated by using two real data sets as well as a simulation study and a simulated data set. Empirical results seem to indicate that the Wald test statistic is less sensitive to atypical returns than maximum likelihood estimators of the slopes. By the other hand, there is some evidence about the convenience of jointly using first and second-order influence measures, to detect months/days with outlying returns, principally in Wald test statistic. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study inference in an heteroskedastic calibration model. We embrace a multivariate structural model with known diagonal covariance error matrices, which is a common setup when different measurement methods are compared. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators and a graphical device for model checking are also discussed. Test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. Results of simulations comprising point estimation, interval estimation, and hypothesis testing are reported. An application to a real data set is given. Up to best of our knowledge, topics such as model checking and hypotheses testing have received only scarce attention in the literature on calibration models. [ABSTRACT FROM AUTHOR]