Working paper
Working paper · 2022
Abstract
We propose a joint significance of many coefficients in high-dimensional linear regression that is robust to unconditional heteroskedasticity and autocorrelation of unknown form within regression errors. Exploiting information on the limiting behaviors of an equally weighted empirical spectral distribution with its weighted counterpart, we derive the asymptotic property of proposed statistics without a priori knowledge of the sparsity level of tested parameters and the underlying structure of regression errors. Instead, we adopt the Random Matrix Theory and self-normalization technique to comprehend the curse of dimensionality, heteroskedasticity, and autocorrelation simultaneously. Thanks to the naturality of parametric framework, the limiting Gaussian distribution of our proposed statistics are free from the choice of kernel functions and bandwidth selections. Simulation studies confirm the accuracy of type-I error with satisfactory empirical testing power in a finite sample over many different types of dependent data such as time-series data and spatially dependent data. In practice, to avoid an upward size distortion from using conventional statistics, we recommend practitioners take the curse of dimensionality into account when the intensity ratio is greater than 0.05.