Effect of dependence on stochastic measures of accuracy of density estimations
依赖性对密度估计随机精度度量的影响AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究高斯过程函数的长短期依赖及其对估计和带宽的影响，直接对应时间序列方法，但未指定宏观应用。
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依赖性对密度估计随机精度度量的影响
- 研究问题
- 对于高斯过程的函数构成的依赖数据，长期依赖如何影响核密度估计的单次实现误差、最优带宽及交叉验证带宽？
- 方法与思路
- 作者区分跨实现平均的风险评估与单次实现的随机误差分析，考察长短记忆分界附近的收敛率和带宽渐近性质。
- 材料陈述的贡献
- 摘要称长期依赖对随机误差可更早产生影响，并改变两类最优带宽的距离及交叉验证带宽的方差和极限相关关系。
- 阅读关注点
- 应核对高斯过程及其函数的限制、长记忆参数和带宽条件，区分 ISE 与 MISE，并查清带宽极限相关结论的适用情形。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；相关结论限定于所述高斯过程函数框架，具体阶数和条件未给出，不能推广到任意依赖数据。
原文摘要
In kernel density estimation, those data values that make a nondegenerate contribution to the estimator (computed at a given point) tend to be spaced well apart. This property has the effect of suppressing many of the conventional consequences of long-range dependence, for example, slower rates of convergence, which might otherwise be revealed by a traditional loss-or risk-based assessment of performance. From that viewpoint, dependence has to be very long-range indeed before a density estimator experiences any first-order effects. However, an analysis in terms of the convergence rate for a particular realization, rather than the rate averaged over all realizations, reveals a very different picture. We show that from that viewpoint, and in the context of functions of Gaussian processes, effects on rates of convergence can become apparent as soon as the boundary between short- and long-range dependence is crossed. For example, the distance between ISE- and MISE-optimal bandwidths is generally of larger order for long-range dependent data. We shed new light on cross-validation, too. In particular we show that the variance of the cross-validation bandwidth is generally larger for long-range dependent data, and that the first-order properties of this bandwidth do not depend on how many data are left out when constructing the cross-validation criterion. Moreover, for long-range dependent data the cross-validation bandwidth is usually perfectly negatively correlated, in the limit, with the optimal stochastic bandwidth.