We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are automatically boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the estimators, offering nonasymptotic characterizations of both probability concentration and distributional approximation. In particular, we establish optimal uniform convergence rate in probability and valid Gaussian distributional approximations for the t-statistic process indexed over the data support. We also discuss implementation issues such as consistent estimation of the covariance function of the Gaussian approximation, optimal integrated mean squared error bandwidth selection, and valid robust bias-corrected inference. We illustrate the applicability of our results by constructing valid confidence bands and hypothesis tests for both parametric specification and shape constraints, explicitly characterizing their nonasymptotic approximation probability errors. A companion R software package implementing our main results is provided.
翻译:我们首先采用基于本地多元度技术的有条件密度估计值。 估计值是自动的边界适应和容易执行的。 然后我们研究估计值的( 点和) 统一统计属性, 提供概率集中和分布近似的非暂时性特征, 特别是, 我们为数据支持指数化的统计进程建立最佳的概率统一率和有效的高斯分布近似值。 我们还讨论执行问题, 如一致估计高斯近似值的共变量、 最佳集成平均正方形误差带选择, 以及有效的稳健的偏差推断值。 我们通过建立有效的信任带和假设测试来说明我们的结果的适用性, 包括参数规格和形状限制, 明确描述其非随机近似概率误差。 我们提供了执行我们主要结果的配套的 R 软件包 。