Another look at bandwidth-free inference: a sample splitting approach
针对多维参数无带宽检验在小样本下因维度和时间依赖导致尺寸扭曲的问题，提出样本分割方法将参数降维至一维，适用于均值检验、零自相关检验等，并通过模拟验证其有效性。
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.