论文标题
单调性的多元非参数回归模型中的自适应推断
Adaptive Inference in Multivariate Nonparametric Regression Models Under Monotonicity
论文作者
论文摘要
我们考虑在多元非参数回归设置下某个点上对回归函数的自适应推断问题。回归函数属于Hölder类，相对于某些或全部参数是单调的。我们得出适应潜在平滑度的置信区间（CI）的最小收敛速率，并提供了获得该最小值速率的自适应推理程序。该程序与CAI和Low（2004）的程序不同，旨在在实际相关规格下产生较短的CI。该提出的方法适用于回归函数的一般线性功能，与现有推理程序相比，该方法具有优惠的性能。
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a Hölder class and is assumed to be monotone with respect to some or all of the arguments. We derive the minimax rate of convergence for confidence intervals (CIs) that adapt to the underlying smoothness, and provide an adaptive inference procedure that obtains this minimax rate. The procedure differs from that of Cai and Low (2004), intended to yield shorter CIs under practically relevant specifications. The proposed method applies to general linear functionals of the regression function, and is shown to have favorable performance compared to existing inference procedures.
