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有限总体中的分位数过程及其应用AI 解读

The weak convergence of the quantile processes, which are constructed based on different estimators of the finite population quantiles, is shown under various well-known sampling designs based on a superpopulation model. The results related to the weak convergence of these quantile processes are applied to find asymptotic distributions of the smooth L-estimators and the estimators of smooth functions of finite population quantiles. Based on these asymptotic distributions,…

基于均值、空间符号与空间秩的高维数据检验AI 解读

Tests based on mean vectors and spatial signs and ranks for a zero mean in one-sample problems and for the equality of means in two-sample problems have been studied in the recent literature for high-dimensional data with the dimension larger than the sample size. For the above testing problems, we show that under suitable sequences of alternatives, the powers of the mean-based tests and the tests based on spatial signs and ranks tend to be same as the data dimension tends…

无限维空间中的空间分布、分位数与深度AI 解读

The spatial distribution has been widely used to develop various nonparametric procedures for finite dimensional multivariate data. In this paper, we investigate the concept of spatial distribution for data in infinite dimensional Banach spaces. Many technical difficulties are encountered in such spaces that are primarily due to the noncompactness of the closed unit ball. In this work, we prove some Glivenko–Cantelli and Donsker-type results for the empirical spatial…

回归中协变量的分位位置变换AI 解读

The need for comparing two regression functions arises frequently in statistical applications. Comparison of the usual regression functions is not very meaningful in situations where the distributions and the ranges of the covariates are different for the populations. For instance, in econometric studies, the prices of commodities and people's incomes observed at different time points may not be on comparable scales due to inflation and other economic factors. In this…

曲线估计的尺度空间视角AI 解读

Scale space theory from computer vision leads to an interesting and novel approach to nonparametric curve estimation. The family of smooth curve estimates indexed by the smoothing parameter can be represented as a surface called the scale space surface. The smoothing parameter here plays the same role as that played by the scale of resolution in a visual system. In this paper, we study in detail various features of that surface from a statistical viewpoint. Weak convergence…

平均导数分位数回归AI 解读

For fixed $\alpha \epsilon (0, 1)$, the quantile regression function gives the $\alpha$th quantile $\theta_{\alpha}(\mathbf{x})$ in the conditional distribution of a response variable Y given the value $\mathbf{X} = \mathbf{x}$ of a vector of covariates. It can be used to measure the effect of covariates not only in the center of a population, but also in the upper and lower tails. A functional that summarizes key features of the quantile specific relationship between X and…

多元数据分位数的几何定义AI 解读

An extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered. The approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles, both of which have been extensively studied in the literature. These geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other L estimates of…

多维符号检验：基于数据点云几何的推断AI 解读

Multivariate sign tests attracted several statisticians in the past, and it is evident from recent nonparametric literature that they still continue to draw attention. One of the most important features of the univariate sign test is that it does not involve much technical assumptions or complicacy, and this makes it quite popular among statistics users. In this article we have come up with a new method for constructing multivariate sign tests that have reasonable…

非线性实验：最优设计与基于似然的推断AI 解读

Nonlinear experiments involve response and regressors that are connected through a nonlinear regression-type structure. Examples of nonlinear models include standard nonlinear regression, logistic regression, probit regression. Poisson regression, gamma regression, inverse Gaussian regression, and so on. The Fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest. As a result, we face an awkward…

通过 U 统计量型方法扩展 R 估计的多元位置估计AI 解读

We consider a class of $U$-statistics type estimates for multivariate location. The estimates extend some $R$-estimates to multivariate data. In particular, the class of estimates includes the multivariate median considered by Gini and Galvani (1929) and Haldane (1948) and a multivariate extension of the well-known Hodges-Lehmann (1963) estimate. We explore large sample behavior of these estimates by deriving a Bahadur type representation for them. In the process of…

回归分位数的非参数估计及局部 Bahadur 表示AI 解读

Let $(X, Y)$ be a random vector such that $X$ is $d$-dimensional, $Y$ is real valued and $Y = \theta(X) + \varepsilon$, where $X$ and $\varepsilon$ are independent and the $\alpha$th quantile of $\varepsilon$ is $0$ ($\alpha$ is fixed such that $0 < \alpha < 1$). Assume that $\theta$ is a smooth function with order of smoothness $p > 0$, and set $r = (p - m)/(2p + d)$, where $m$ is a nonnegative integer smaller than $p$. Let $T(\theta)$ denote a derivative of $\theta$ of…