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多属性洛伦兹函数与基尼指数：测度运输方法AI 解读

Based on measure transportation ideas and the related concepts of quantile functions and regions, we propose multiple-output generalizations of the traditional univariate concepts of Lorenz and concentration functions, and the related Gini and Kakwani coefficients. These new concepts have a natural interpretation, either in terms of contributions of quantile regions to the expectation of some variable of interest, or in terms of the physical notions of work and energy, which…

非参数多输出中心向外分位数回归AI 解读

–Building on recent measure-transportation-based concepts of multivariate quantiles, we are considering the problem of nonparametric multiple-output quantile regression. Our approach defines nested conditional center-outward quantile regression contours and regions with given conditional probability content, the graphs of which constitute nested center-outward quantile regression tubes with given unconditional probability content; these (conditional and unconditional)…

Monge–Kantorovich 深度、分位数、秩与符号AI 解读

We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks and signs, based on canonical transportation maps between a distribution of interest on $\mathbb{R}^{d}$ and a reference distribution on the $d$-dimensional unit ball. The new depth concept, called Monge–Kantorovich depth, specializes to halfspace depth for $d=1$ and in the case of spherical distributions, but for more general distributions, differs from the latter in the…

中位数约束模型中基于符号与秩的半参数有效推断AI 解读

Summary Since the pioneering work of Koenker and Bassett, median-restricted models have attracted considerable interest. Attention in these models, so far, has focused on least absolute deviation (auto-)regression quantile estimation and the corresponding sign tests. These methods use a pseudolikelihood that is based on a double-exponential reference density and enjoy quite attractive properties of root n consistency (for estimators) and distribution freeness (for tests).…

A local linear kernel estimator of the regression function x↦g(x):=E[Yi|Xi=x], x∈ℝd, of a stationary (d+1)-dimensional spatial process {(Y i,Xi),i∈ℤN} observed over a rectangular domain of the form ℐn:={i=(i1,…,iN)∈ℤN|1≤ik≤nk,k=1,…,N}, n=(n1,…,nN)∈ℤN, is proposed and investigated. Under mild regularity assumptions, asymptotic normality of the estimators of g(x) and its derivatives is established. Appropriate choices of the bandwidths are proposed. The spatial process is…