The purpose of regression analysis is to expose the relationship between a response variable and predictor variables. In real applications, the response variable cannot be predicted exactly from the predictor variables. Instead, the response for a fixed value of each predictor variable is a random variable. For this reason, we often summarize the behavior of the response for fixed values of the...

Fuzziness is discussed in the context of multivalued lo&, and a corresponding view of fuzzy sets is given. Fuzzy random variables are introduced as random variables whose values are not real but fuzzy numbers, and subsequently redefined as a particular kind of fuzzy set. Expectations of fuzzy random variables, characteristic f~cti~ of fuzzy events, probabilities connected to fuzzy random variab...

The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption is not always fulfilled. An alternative approach is random forests for survival outcomes. The standard split criterion for random survival forests is the log-rank test statistics, which favors splitting variables with many possible sp...

Optimality conditions are derived for problems of minimizing a generalized measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. Generalized measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optima...

The problem of the nonparametric local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space is considered. Some theoretical and practical asymptotic properties of this estimator are established. The usefulness of the estimator is highlighted through the exact expression involved in the leading terms of the quadra...

Optimality conditions are derived for problems of minimizing a general measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. General measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optimality con...

This article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors. Goals are (1) to estimate the conditional response distribution addressing the distributional changes across the predictor space, and (2) to identify important predictors for the response distribution change both within local regions and globally. We first introduce the ...

This paper studies vector quantile regression (VQR), which is a way to model the dependence of a random vector of interest with respect to a vector of explanatory variables so to capture the whole conditional distribution, and not only the conditional mean. The problem of vector quantile regression is formulated as an optimal transport problem subject to an additional mean-independence conditio...

Consider the random vector (X,Y ), where Y represents a response variable and X an explanatory variable. The response Y is subject to random right censoring, whereas X is completely observed. Let m(x) be a conditional location function of Y given X = x. In this paper we assume that m(·) belongs to some parametric class M = {mθ : θ ∈ Θ} and we propose a new method for estimating the true unknown...

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random Gexpectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent li...