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
- 在样本量有限且参数维度与时间依赖均不低时，如何缓解现有免带宽检验的尺寸扭曲，并保留易于实施的推断方式？
- 方法与思路
- 作者用样本分割将后续推断对象降为一维，再结合自归一化构造 L∞ 型和 L2 型检验，分析固定及增长维度下的极限行为。
- 材料陈述的贡献
- 摘要称模拟显示尺寸扭曲得到缓解，并建立增长维度均值检验的极限分布及两类统计量在零假设下的渐近独立性。
- 阅读关注点
- 应核对分割方式、降维方向如何确定及分割间依赖处理，并检查维度增长与序列依赖限制，以及改善尺寸所付出的功效代价。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出增长率条件、尺寸数值或分割规则，不能认为免带宽即可保证有限样本可靠。
原文摘要
The bandwidth-free tests/inferences 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 HAC-based approaches, where consistent long run variance estimation was involved. 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-normalization) idea is broadly applicable to many testing problems for time series, including mean testing, testing for zero autocorrelation, linear hypotheses testing in a time series regression model and testing for a change point in multivariate mean. Specifically, we propose $L_{\infty}$-type and $L_2$-type 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. As an important theoretical contribution, we obtain the limiting distributions for both SS-SN test statistics in the multivariate mean testing problem when the dimension is allowed to diverge as sample size grows to infinity. In addition we show the asymptotic independence of $L_{\infty}$-type and $L_2$-type SS-SN test statistics under the null in the growing dimensional setting.