论文标题
在回归器多订购下的回归残差之和的渐近分数
Asymptotics of sums of regression residuals under multiple ordering of regressors
论文作者
论文摘要
我们证明了有关由带有多个回归器排序的线性模型回归器构建的经验桥的高斯渐近学定理。我们研究了随机向量组件的线性模型的假设的测试：其中一个组件是其他词的线性组合，直到不取决于随机向量的其他成分。观察随机载体的独立副本的结果按其几个成分的上升顺序顺序排序。结果是一系列较高维度的向量序列，该矢量由与不同顺序相对应的诱导顺序统计（伴随）组成。对于这种矢量序列，没有假设组件的线性模型，我们证明了适当中心和归一化的过程对与几乎连续轨迹的中心高斯过程的分布的弱收敛性的引理。假设组件的线性关系，标准最小二乘估计值用于计算回归残差 - 响应值与线性模型预测值之间的差异。我们证明了在必要的归一化水平过程中回归残差过程弱收敛的定理。
We prove theorems about the Gaussian asymptotics of an empirical bridge built from linear model regressors with multiple regressor ordering. We study the testing of the hypothesis of a linear model for the components of a random vector: one of the components is a linear combination of the others up to an error that does not depend on the other components of the random vector. The results of observations of independent copies of a random vector are sequentially ordered in ascending order of several of its components. The result is a sequence of vectors of higher dimension, consisting of induced order statistics (concomitants) corresponding to different orderings. For this sequence of vectors, without the assumption of a linear model for the components, we prove a lemma of weak convergence of the distributions of an appropriately centered and normalized process to a centered Gaussian process with almost surely continuous trajectories. Assuming a linear relationship of the components, standard least squares estimates are used to compute regression residuals -- the differences between response values and the predicted ones by the linear model. We prove a theorem of weak convergence of the process of regression residuals under the necessary normalization to a centered Gaussian process.
