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首页> 外文期刊>Journal of Econometrics >Local Rank Tests in a Multivariate Nonparametric Relationship.
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Local Rank Tests in a Multivariate Nonparametric Relationship.

机译:多元非参数关系中的本地等级检验。

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摘要

Consider a multivariate nonparametric model where the unknown vector of functions depends on two sets of explanatory variables. For a fixed level of one set of explanatory variables, we provide consistent statistical tests, called local rank tests, to determine whether the multivariate relationship can be explained by a smaller number of functions. We also provide estimators for the smallest number of functions, called local rank, explaining the relationship. The local rank tests and the estimators of local rank are defined in terms of the eigenvalues of a kernel-based estimator of some matrix. The asymptotics of the eigenvalues is established by using the so-called Fujikoshi expansion along with some techniques of the theory of U-statistics. We present a simulation study which examines the small sample properties of local rank tests. We also apply the local rank tests and the local rank estimators to a demand system given by a newly constructed data set. This work can be viewed as a "local" extension of the tests for a number of factors in a nonparametric relationship introduced by Stephen Donald.
机译:考虑一个多元非参数模型,其中函数的未知向量取决于两组解释变量。对于固定水平的一组解释变量,我们提供一致的统计检验(称为局部等级检验),以确定是否可以用较少数量的函数解释多元关系。我们还为最小数量的函数(称为局部等级)提供了估算器,以解释这种关系。局部秩检验和局部秩的估计器是根据某个矩阵的基于核的估计器的特征值来定义的。特征值的渐近性是通过使用所谓的Fujikoshi展开以及U统计理论的一些技术来建立的。我们提供了一个模拟研究,该研究检查了本地等级测试的小样本属性。我们还将局部等级检验和局部等级估计应用于由新构建的数据集提供的需求系统。可以将这项工作视为斯蒂芬·唐纳德(Stephen Donald)引入的非参数关系中许多因素的测试的“局部”扩展。

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