We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the estimators, offering characterizations of both probability concentration and distributional approximation. In particular, we establish uniform convergence rates in probability and valid Gaussian distributional approximations for the Studentized t-statistic process. We also discuss implementation issues such as consistent estimation of the covariance function for 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 approximation errors. A companion R software package implementing our main results is provided.

翻译：我们首先介绍一类基于局部多项式技术的条件密度估计器。此类估计器具有边界自适应性且易于实现。随后我们研究估计量的（逐点及）一致统计性质，分别刻画其概率集中性与分布逼近特性。具体而言，我们建立了概率意义下的一致收敛速率，并证明了学生化t统计量过程的高斯分布逼近有效性。在实施层面，我们讨论了高斯逼近协方差函数的一致估计、最优积分均方误差带宽选择，以及稳健的偏差校正推断方法。通过构建参数设定与形状约束下的有效置信带与假设检验方法，并显式刻画其逼近误差，我们展示了研究成果的适用性。配套的R语言软件包已提供，可实现主要结论。