Related papers: A quantile-based probabilistic mean value theorem
The concept of mean inactivity time plays a crucial role in reliability, risk theory and life testing. In this regard, we introduce a weighted mean inactivity time function by considering a non-negative weight function. Based on this…
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are…
Taylor's law (TL) states that the variance $V$ of a non-negative random variable is a power function of its mean $M$, i.e. $V=a M^b$. The ubiquitous empirical verification of TL, typically displaying sample exponents $b \simeq 2$, suggests…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
All multivariate extensions of the univariate theory of risk measurement run into the same fundamental problem of the absence, in dimension d > 1, of a canonical ordering of Rd. Based on measure transportation ideas, several attempts have…
Since the pioneering work by Koenker and Bassett (1978), quantile regression models and its applications have become increasingly popular and important for research in many areas. In this paper, a random effects ordinal quantile regression…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Quantile regression (QR) is now widely used to analyze the effect of covariates on the conditional distribution of a response variable. It provides a more comprehensive picture of the relationship between a response and covariates compared…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
A new four-parameter model called the Marshall-Olkin extended generalized Gompertz distribution is introduced. Its hazard rate function can be constant, increasing, decreasing, upside-down bathtub or bathtub-shaped depending on its…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those…
In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of…
This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple…
Quantile-based classifiers can classify high-dimensional observations by minimising a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
In a recent study of large non-null sample covariance matrices, a new sequence of functions generalizing the GUE Tracy-Widom distribution of random matrix theory was obtained. This paper derives Painlev\'e formulas of these functions and…
We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions,…