Related papers: Conditional Expectation as Quantile Derivative
Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…
Value at risk and expected shortfall are increasingly popular tail risk measures in the financial risk management field. Both academia and financial institutions are working to improve tail risk forecasts in order to meet the requirements…
This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a…
This paper introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized GARCH model and employ…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…
The so-called pinball loss for estimating conditional quantiles is a well-known tool in both statistics and machine learning. So far, however, only little work has been done to quantify the efficiency of this tool for nonparametric…
Estimating the conditional quantile of the interested variable with respect to changes in the covariates is frequent in many economical applications as it can offer a comprehensive insight. In this paper, we propose a novel semiparametric…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree 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…
This paper develops estimation and inference methods for conditional quantile factor models. We first introduce a simple sieve estimation, and establish asymptotic properties of the estimators under large $N$. We then provide a bootstrap…
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
Quantile Regression (QR) provides a way to approximate a single conditional quantile. To have a more informative description of the conditional distribution, QR can be merged with deep learning techniques to simultaneously estimate multiple…
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…