Uniform Inference for Kernel Density Estimators with Dyadic Data
成对关系数据核密度估计的一致推断AI 解读 ↓
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成对关系数据核密度估计的一致推断
- 研究问题
- 当观测对应网络边且存在成对依赖时，如何对未知密度作全域估计与置信带推断，并处理支持集上可能出现的退化点？
- 方法与思路
- 作者研究成对经验过程形式的核密度估计，建立强逼近与方差估计，并结合协方差处理、带宽选择和稳健偏差校正。
- 材料陈述的贡献
- 摘要称给出极小极大最优的一致收敛速率及可行置信带，允许退化点，并扩展至反事实密度推断和贸易分布比较。
- 阅读关注点
- 应核对网络依赖结构、退化的数学定义、置信带覆盖条件，以及反事实分布的识别要求与带宽、协方差估计的实现。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未列出具体依赖和识别假设，退化稳健性不代表适用任意网络。
原文摘要
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of uniformly estimating a dyadic Lebesgue density function, focusing on nonparametric kernel-based estimators taking the form of dyadic empirical processes. Our main contributions include the minimax-optimal uniform convergence rate of the dyadic kernel density estimator, along with strong approximation results for the associated standardized and Studentized $t$-processes. A consistent variance estimator enables the construction of valid and feasible uniform confidence bands for the unknown density function. We showcase the broad applicability of our results by developing novel counterfactual density estimation and inference methodology for dyadic data, which can be used for causal inference and program evaluation. A crucial feature of dyadic distributions is that they may be "degenerate" at certain points in the support of the data, a property making our analysis somewhat delicate. Nonetheless our methods for uniform inference remain robust to the potential presence of such points. For implementation purposes, we discuss inference procedures based on positive semi-definite covariance estimators, mean squared error optimal bandwidth selectors and robust bias correction techniques. We illustrate the empirical finite-sample performance of our methods both in simulations and with real-world trade data, for which we make comparisons between observed and counterfactual trade distributions in different years. Our technical results concerning strong approximations and maximal inequalities are of potential independent interest.