Felipe Osorio

1. It is well known that outlying observations can have a disproportionate effect on various aspects of statistical modelling-namely, parameter estimation, goodness of fit, and inferential results....

The invariance properties of certain likelihood-based asymptotic tests as well as their extensions for M-estimation, estimating functions and the generalized method of moments have been well studied. The simulation study reported in Crudu and Osorio [Econ. Lett. 187: 108885, 2020] shows that the bilinear form test is not invariant to one-to-one transformations of the parameter space. This paper provides a set of suitable conditions to establish the invariance property under reparametrization of the bilinear form test for linear or nonlinear hypotheses that arise in extremum estimation which leads to a simple modification of the test statistic. Evidence from a Monte Carlo simulation experiment suggests good performance of the proposed methodology.

The Box-Cox transformation, introduced in 1964, is a widely used statistical tool for stabilizing variance and improving normality in data analysis. Its application in image processing, particularly for image enhancement, has gained increasing attention in recent years. This paper investigates the use of the Box-Cox transformation as a preprocessing step for image segmentation, with a focus on the estimation of the transformation parameter. We evaluate the effectiveness of the transformation by comparing various segmentation methods, highlighting its advantages for traditional machine learning techniques-especially in situations where no training data is available. The results demonstrate that the transformation enhances feature separability and computational efficiency, making it particularly beneficial for models like discriminant analysis. In contrast, deep learning models did not show consistent improvements, underscoring the differing impacts of the transformation across model types and image characteristics.

In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual iteratively weighted least squares method in generalized linear models is presented. It is through the discussion of the asymptotic distribution of the proposed estimator and a set of statistics for testing linear hypothesis that it is possible to define standardized residuals using the mean-shift outlier model. In addition, robust versions of deviance function and the Akaike information criterion are defined with the aim of providing tools for model selection. Finally, the performance of the proposed methodology is illustrated through a simulation study and analysis of a real dataset.

Computing the agreement between 2 continuous sequences is of great interest in statistics when comparing 2 instruments or one instrument with a gold standard. The probability of agreement quantifies the similarity between 2 variables of interest, and it is useful for determining what constitutes a practically important difference. In this article, we introduce a generalization of the PA for the treatment of spatial variables. Our proposal makes the PA dependent on the spatial lag. We establish the conditions for which the PA decays as a function of the distance lag for isotropic stationary and nonstationary spatial processes. Estimation is addressed through a first-order approximation that guarantees the asymptotic normality of the sample version of the PA. The sensitivity of the PA with respect to the covariance parameters is studied for finite sample size. The new method is described and illustrated with real data involving autumnal changes in the green chromatic coordinate (G_cc), an index of “greenness” that captures the phenological stage of tree leaves, is associated with carbon flux from ecosystems, and is estimated from repeated images of forest canopies.