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  1. A novel statistical method is proposed and investigated for estimating a heavy tailed density under mildsmoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem ofsparse 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 regularizationthrough a carefully specified semiparametric prior distribution, and is able to consistently estimate boththe density function and its tail index at near minimax optimal rates of contraction. A joint, likelihood drivenestimation of the bulk and the tail is shown to help improve uncertainty assessment in estimating the tailindex parameter and offer more accurate and reliable estimates of the high tail quantiles compared tothresholding methods. Supplementary materials for this article are available online. 
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