Heavy-Tailed Density Estimation
提出一种新的贝叶斯方法，在温和光滑性假设下估计重尾密度，通过半参数先验实现光滑性和尾部正则化，以接近最优速率一致估计密度函数和尾部指数，并改善高尾分位数的估计精度。
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk. The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularization through a carefully specified semiparametric prior distribution, and is able to consistently estimate both the density function and its tail index at near minimax optimal rates of contraction. A joint, likelihood driven estimation of the bulk and the tail is shown to help improve uncertainty assessment in estimating the tail index parameter and offer more accurate and reliable estimates of the high tail quantiles compared to thresholding methods. Supplementary materials for this article are available online.