Another look at bandwidth-free inference: a sample splitting approach
重新审视免带宽推断：样本分割方法AI 解读 ↓
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重新审视免带宽推断：样本分割方法
- 研究问题
- 小中样本下，参数维度与时间依赖均适中时免带宽检验可能产生较大尺寸失真，能否通过样本分割和降维改善推断？
- 方法与思路
- 作者先用样本分割将后续检验的参数维度降至一维，再结合自归一化构造两类 SS–SN 统计量，分析原假设与备择下的分布。
- 材料陈述的贡献
- 摘要称得到两类统计量的极限分布，模拟显示尺寸失真有所缓解，并给出多元均值检验中参数维度发散时的极限结果。
- 阅读关注点
- 应核对分割比例、时间依赖条件、降维步骤与检验功效的关系，以及均值变化点检验和维度发散结论各自的适用条件。
- 阅读边界
- 仅据所给 Crossref 摘要，无法判断尺寸改善的幅度、功效代价或维度增长限制；不能据此认定所有依赖结构下均有效。
原文摘要
Abstract The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the dimension of the parameter and the magnitude of temporal dependence are moderate, making them unreliable to use in practice. In this paper, we propose a sample splitting-based approach to reduce the dimension of the parameter to one for the subsequent bandwidth-free inference. Our SS–SN (sample splitting plus self-normalisation) idea is broadly applicable to many testing problems for time series, including mean testing, testing for zero autocorrelation, and testing for a change point in multivariate mean, among others. Specifically, we propose two types of SS–SN test statistics and derive their limiting distributions under both the null and alternatives and show their effectiveness in alleviating size distortion via simulations. In addition, we obtain the limiting distributions for both SS–SN test statistics in the multivariate mean testing problem when the dimension is allowed to diverge.