SPECTRAL DENSITY ESTIMATION AND ROBUST HYPOTHESIS TESTING USING STEEP ORIGIN KERNELS WITHOUT TRUNCATION*
提出一种通过对传统二次核取指数得到的新核函数，用于长期方差和谱密度估计。当指数参数随样本量增大时估计量一致且渐近正态；指数固定时估计量不一致但有非标准极限分布。蒙特卡洛实验表明，指数较小时非标准极限理论能更好逼近有限样本分布，对回归中的谱密度估计和检验统计量有用。
A new class of kernels for long‐run variance and spectral density estimation is developed by exponentiating traditional quadratic kernels. Depending on whether the exponent parameter is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimators. When the exponent is passed to infinity with the sample size, the new estimator is consistent and shown to be asymptotically normal. When the exponent is fixed, the new estimator is inconsistent and has a nonstandard limiting distribution. It is shown via Monte Carlo experiments that, when the chosen exponent is small in practical applications, the nonstandard limit theory provides better approximations to the finite sample distributions of the spectral density estimator and the associated test statistic in regression settings.