EDGEWORTH EXPANSIONS FOR SPECTRAL DENSITY ESTIMATES AND STUDENTIZED SAMPLE MEAN
为平滑非参数谱密度估计和学生化线性统计量（如样本均值）的分布建立了有效的埃奇沃思展开，特别关注零频率处的谱估计，以改进正态近似并给出可行的带宽选择规则。
We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the sample mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our main focus is on stationary Gaussian series, though we discuss relaxation of the Gaussianity assumption. Only smoothness conditions on the spectral density that are local to the frequency of interest are imposed. We deduce empirical expansions from our Edgeworth expansions designed to improve on the normal approximation in practice and also deduce a feasible rule of bandwidth choice.