Local Gaussian Correlation in the Tails: A Scarcity Diagnostic, an Optimal Local Bandwidth, and the Limits of Adaptivity
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尾部局部高斯相关：样本稀缺诊断、最优局部带宽与适应性的边界
- 研究问题
- 联合尾部的局部高斯相关估计为何不稳定，位置自适应带宽何时能改善估计，又何时受到有效样本稀缺的限制？
- 方法与思路
- 作者结合局部有效样本诊断、局部似然渐近展开和位置特定最优带宽，利用不同依赖强度的模拟及过滤后股票收益进行比较。
- 材料陈述的贡献
- 摘要称，自适应带宽仅在中等依赖且相关曲面弯曲时改善表现；尾部信息稀缺是主要约束，股票应用中重抽样曲面更稳定。
- 阅读关注点
- 应核对有效样本量的定义、偏差展开与带宽公式的条件，以及强依赖下误差随样本量增大的机制和金融应用的过滤步骤。
- 阅读边界
- 这是预印本，不能据此认定已同行评审或期刊接收。摘要中的带宽优劣具有场景限制，未说明全部条件与应用不确定性。
原文摘要
Local Gaussian correlation (LGC) measures dependence locally, making it a natural tool for tail dependence and financial contagion, but its estimates degrade in the joint tails, where they are most needed. Location-adaptive bandwidths have been tried for LGC and found inferior to a single global bandwidth; we explain why, and map the regime in which adaptivity does help. First, a diagnostic: across heavy-tailed data-generating processes the parametric marginal pre-transform is inert (it changes the integrated error only in the fourth decimal), while the binding constraint is the local effective sample size, with the replication dispersion following a Fisher variance floor sd ~ (1 - rho^2)/sqrt(eff_n). Second, theory: specializing the Hjort-Jones local-likelihood asymptotics to the bivariate Gaussian family that LGC fits, we derive the first location-specific AMISE-optimal bandwidth for LGC, b*(x) proportional to [(1 - rho^2)^2 / (f beta^2)]^(1/6) n^(-1/6), and validate its bias expansion directly (bias proportional to b^2 beta, R^2 approximately 0.9, slope-to-beta correlation 0.80). Third, a regime map: a Monte Carlo across dependence strengths shows the adaptive rule beats the global plug-in only at moderate dependence with curved surfaces. At weak dependence there is no curvature to exploit; at strong dependence finite-sample bias from the steep surface dominates, and adaptivity performs substantially worse, with an error that grows in the sample size. This explains the field's experience that global bandwidths are hard to beat, and locates the exception. Fourth, application: on volatility-filtered equity returns the adaptive estimator yields more stable tail-dependence surfaces under resampling. The message is cautionary: the binding constraint on tail LGC is data scarcity, not bandwidth placement, and no bandwidth, however optimal, can recover information the data do not contain.