Related papers: From Halfspace M-depth to Multiple-output Expectil…
Expectiles were introduced by Newey and Powell (1987) in the context of linear regression models. Recently, Bellini et al. (2014) revealed that expectiles can also be seen as reasonable law-invariant risk measures. In this article, we show…
It is common in machine learning to estimate a response $y$ given covariate information $x$. However, these predictions alone do not quantify any uncertainty associated with said predictions. One way to overcome this deficiency is with…
We examine the problem of computing multivariate scenarios sets for skewed distributions. Our interest is motivated by the potential use of such sets in the "stress testing" of insurance companies and banks whose solvency is dependent on…
We show that the estimating equations for quantile regression can be solved using a simple EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…
Tukey's depth offers a powerful tool for nonparametric inference and estimation, but also encounters serious computational and methodological difficulties in modern statistical data analysis. This paper studies how to generalize and compute…
The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…
Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…
Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…
Statistical inference in high-dimensional settings is challenging when standard unregularized methods are employed. In this work, we focus on the case of multiple correlated proportions for which we develop a Bayesian inference framework.…
Distributional regression aims to estimate the full conditional distribution of a target variable, given covariates. Popular methods include linear and tree-ensemble based quantile regression. We propose a neural network-based…
We develop a novel exploratory tool for non-Euclidean object data based on data depth, extending the celebrated Tukey's depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in a general metric space,…
One of the most important studies in finance is to find out whether stock returns could be predicted. This research aims to create a new multivariate model, which includes dividend yield, earnings-to-price ratio, book-to-market ratio as…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
Quantile regression \parencite{Koenker1978} is a robust and practically useful way to efficiently model quantile varying correlation and predict varied response quantiles of interest. This article constructs and tests MM algorithms, which…
We develop quantile regression methods for discrete responses by extending Parzen's definition of marginal mid-quantiles. As opposed to existing approaches, which are based on either jittering or latent constructs, we use interpolation and…
In 1975 John Tukey proposed a multivariate median which is the 'deepest' point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered…
The concept of depth represents methods to measure how deep an arbitrary point is positioned in a dataset and can be seen as the opposite of outlyingness. It has proved very useful and a wide range of methods have been developed based on…
Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and financial applications. The authors introduce a new semiparametric quantile regression method based on…