Robust Likelihood Cross-Validation for Kernel Density Estimation
针对核密度估计中似然交叉验证对极端值和厚尾分布敏感的问题，提出一种稳健的似然交叉验证方法，通过平滑过渡结合似然与最小二乘交叉验证的优势，并给出阈值选择规则，模拟和空气污染数据验证了其有效性。
Likelihood cross-validation for kernel density estimation is known to be sensitive to extreme observations and heavy-tailed distributions. We propose a robust likelihood-based cross-validation method to select bandwidths in multivariate density estimations. We derive this bandwidth selector within the framework of robust maximum likelihood estimation. This method establishes a smooth transition from likelihood cross-validation for nonextreme observations to least squares cross-validation for extreme observations, thereby combining the efficiency of likelihood cross-validation and the robustness of least-squares cross-validation. We also suggest a simple rule to select the transition threshold. We demonstrate the finite sample performance and practical usefulness of the proposed method via Monte Carlo simulations and a real data application on Chinese air pollution.