尾部的局部高斯相关性：稀缺性诊断、最优局部带宽与适应性极限
Local Gaussian Correlation in the Tails: A Scarcity Diagnostic, an Optimal Local Bandwidth, and the Limits of Adaptivity
AI总结：
研究局部高斯相关性在尾部估计的问题，通过诊断、理论推导得出最优局部带宽，绘制适应性区域图并应用于股票收益，指出尾部估计受数据稀缺限制，最优带宽也无法恢复数据中没有的信息。
AI中文摘要：
局部高斯相关性（LGC）在局部测量依赖性，是尾部依赖性和金融传染的自然工具，但在联合尾部估计会退化。本文解释位置自适应带宽效果不佳的原因并确定适应性起作用的情况，推导最优带宽，绘制区域图并应用于股票收益，表明尾部LGC受数据稀缺限制。
英文摘要：
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.
