标题： 具有许多协变量的点过程预测估计 显示英文标题

标题： Estimation for the Prediction of Point Processes with Many Covariates

摘要： 在非参数框架下考虑点过程强度的估计。 强度测度是未知的，并且依赖于协变量，可能比观测到的跳跃次数多得多。 只观察到计数过程的一个轨迹。 兴趣在于在协变量条件下的强度估计。 协变量的影响通过一个加法模型来建模，其中每个组件可以写成可能未知函数的线性组合。 重点在于预测而非变量筛选。 为了控制估计误差，对这个线性组合的系数施加了条件。 当活跃协变量的数量较大时，收敛率是最优的。 作为应用，估计了新西兰元期货的买入和卖出交易的强度，并提出了一个预测评估的检验。 包括一个模拟以提供对模型和渐近性质的一些有限样本直觉。 显示英文摘要

摘要： Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the counting process is observed. Interest lies in estimating the intensity conditional on the covariates. The impact of the covariates is modelled by an additive model where each component can be written as a linear combination of possibly unknown functions. The focus is on prediction as opposed to variable screening. Conditions are imposed on the coefficients of this linear combination in order to control the estimation error. The rates of convergence are optimal when the number of active covariates is large. As an application, the intensity of the buy and sell trades of the New Zealand dollar futures is estimated and a test for forecast evaluation is presented. A simulation is included to provide some finite sample intuition on the model and asymptotic properties.