Different linearity tests for a regression model with an imprecise response

Recently a new linear regression model with fuzzy response and scalar explanatory variables has been introduced and deeply analyzed. Since the inferences developed for such a model are meaningful only if the relationship is indeed linear, it is important to check the linearity for the regression model. Two different linearity tests have been introduced. The first one is based on the comparison of the simple linear regression model and the nonparametric regression. In details, the test statistic is constructed based on the variability explained by the two models. The second one consists in using the empirical process of the regressors marked by the residuals. Both tests have been analyzed by means of a bootstrap approach. In particular, a wild bootstrap and a residual bootstrap have been investigated

Testing linearity for a regression model with imprecise elements: a power analysis

A linearity test for a simple regression model with imprecise random elements is analyzed. The concept of LR fuzzy random variable is used to formalize imprecise random elements. The proposed linearity test is based on the comparison of the simple linear regression model and the nonparametric regression. In details, based on the variability explained by the above two models, the test statistic is constructed. The asymptotic significance level and the power under local alternatives are established. Since large samples are required to obtain suitable asymptotic results a bootstrap approach is investigated. Furthermore, in order to illustrate how the proposed test works in practice, some simulation and real-life examples are given

Predicting the Risk of Mortality in Children using a Fuzzy-Probabilistic Hybrid Model

Publisher Copyright: © 2022 Corsino Rey et al.Introduction. The mortality risk in children admitted to Pediatric Intensive Care Units (PICU) is usually estimated by means of validated scales, which only include objective data among their items. Human perceptions may also add relevant information to prognosticate the risk of death, and the tool to use this subjective data is fuzzy logic. The objective of our study was to develop a mathematical model to predict mortality risk based on the subjective perception of PICU staff and to evaluate its accuracy compared to validated scales. Methods. A prospective observational study in two PICUs (one in Spain and another in Latvia) was performed. Children were consecutively included regardless of the cause of admission along a two-year period. A fuzzy set program was developed for the PICU staff to record the subjective assessment of the patients' mortality risk expressed through a short range and a long range, both between 0% and 100%. Pediatric Index of Mortality 2 (PIM2) and Therapeutic Intervention Scoring System 28 (TISS28) were also prospectively calculated for each patient. Subjective and objective predictions were compared using the logistic regression analysis. To assess the prognostication ability of the models a stratified B-random K-fold cross-validation was performed. Results. Five hundred ninety-nine patients were included, 308 in Spain (293 survivors, 15 nonsurvivors) and 291 in Latvia (282 survivors, 9 nonsurvivors). The best logistic classification model for subjective information was the one based on MID (midpoint of the short range), whereas objective information was the one based on PIM2. Mortality estimation performance was 86.3% for PIM2, 92.6% for MID, and the combination of MID and PIM2 reached 96.4%. Conclusions. Subjective assessment was as useful as validated scales to estimate the risk of mortality. A hybrid model including fuzzy information and probabilistic scales (PIM2) seems to increase the accuracy of prognosticating mortality in PICU.publishersversionPeer reviewe

Development and validation of an HIV risk exposure and indicator conditions questionnaire to support targeted HIV screening

The aim of our study was to develop a Spanish-structured HIV risk of exposure and indicator conditions (RE&IC) questionnaire. People attending to an emergency room or to a primary clinical care center were offered to participate in a prospective, 1 arm, open label study, in which all enrolled patients filled out our developed questionnaire and were HIV tested. Questionnaire accuracy, feasibility, and reliability were evaluated. Valid paired 5329 HIV RE&IC questionnaire and rapid HIV tests were performed, 69.3% in the primary clinical care center, 49.6% women, median age 37 years old, 74.9% Spaniards, 20.1% Latin-Americans. Confirmed hidden HIV infection was detected in 4.1%, while HIV RE&IC questionnaire was positive in 51.2%. HIV RE&IC questionnaire sensitivity was 100% to predict HIV infection, with a 100% negative predictive value. When considered separately, RE or IC items sensitivity decreases to 86.4% or 91%, and similarly their negative predictive value to 99.9% for both of them. The majority of people studied, 90.8% self-completed HIV RE&IC questionnaire. Median time to complete was 3 minutes. Overall HIV RE&IC questionnaire test-retest Kappa agreement was 0.82 (almost perfect), likewise for IC items 0.89, while for RE items was lower 0.78 (substantial). A feasible and reliable Spanish HIV RE&IC self questionnaire accurately discriminated all non–HIV-infected people without missing any HIV diagnoses, in a low prevalence HIV infection area. The best accuracy and reliability were obtained when combining HIV RE&IC items

Special issue on Fuzzy sets in statistics

EditorialInternational audienceThis special issue is made of a selection of papers related to the use of fuzzy sets in statistics. It follows the CSDA special issue on Fuzzy Statistical Analysis (Coppi et al., 2006). The CSDA has continued publishing papers on this topic (e.g., Frei and Künsch, in press, ter Braak et al., 2009, Govaert and Nadif, 2008, Berget et al., 2008)

Leyes fuertes de los grandes números para variables aleatorias difusas

En la memoria se demuestran varias leyes fuertes de las grandes números para variables aleatorias difusas que generalizan algunas de las ya conocidas, como la ley fuerte para variables aleatorias reales o la ley fuerte para conjuntos aleatorios. Se desarrollan dos técnicas. Una pone de manifiesto la relación de las leyes fuertes para variables aleatorias difusas, y el teorema de Glirenko-Contelli, a través de un vector aleatorio con ciertas características y al que se denomina rector de cambios de niveles. Debido a esa conexión se formaliza la relación entre los conjuntos difusos y las funciones cadlag y se puede definir la distancia de Skorobard entre conjuntos difusos. Mediante esta métrica se establecen algunas relaciones entre diferentes condiciones de medibilidad que se utilizan habitualmente en la definición de variable aleatoria difusa. De esta manera se llega de manera natural a la segunda técnica que consiste a relacionar las variables aleatorias difusas con los elementos aleatoria que toman valores en el espacio de las funciones cadlag; de esta forma se pueden emplear los resultados conocidos en este espacio para demostrar sus análogos en var.aleat.difusas. Finalmente se realizan úmalaciones de algunos modelos empleados