论文标题
重尾密度估计
Heavy-Tailed Density Estimation
论文作者
论文摘要
提出了一种新型的统计方法，并研究了在轻度平滑度假设下估算较重的尾部密度。对重尾分布的统计分析容易受到分布尾部稀疏信息问题的影响，并被大量大量的无关特征冲走。提出的贝叶斯方法通过通过精心指定的半参数先验分布结合平滑度和尾巴正则化来避免此问题，并能够以最小的最佳收缩速率始终如一地估计密度函数及其尾部指数。与阈值方法相比，与底部索引参数估算尾巴参数的不确定性评估并提供了更准确，更可靠的估计值，与阈值方法相比，对大量和尾巴进行了关节驱动的估计，有助于改善不确定性评估。
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.
