标题： 自举法预测区间用于生命表死亡人数的年龄分布 显示英文标题

标题： Bootstrap prediction intervals for the age distribution of life-table death counts

摘要： 我们引入了一种基于动态因子模型的非参数Bootstrap过程，以构建周期生命表死亡人数的点预测区间。 死亡人数的年龄分布是一个约束数据的例子，这些数据是非负的且具有约束积分。 使用中心对数比变换来消除约束。 在无约束数据的时间序列基础上，我们引入了Bootstrap方法来构建预测区间，从而量化预测不确定性。 Bootstrap方法利用动态因子模型通过两阶段函数主成分分析来捕捉非平稳和平稳模式。 为了捕捉参数不确定性，估计的主成分得分和模型残差是带替换抽样的。 使用澳大利亚和英国的年龄和性别特定的生命表死亡数据，我们研究了经验覆盖概率并将其与名义概率进行比较。 Bootstrap方法在区间预测准确性方面表现更优，尤其是在一步 ahead 预测范围内。 显示英文摘要

摘要： We introduce a nonparametric bootstrap procedure based on a dynamic factor model to construct pointwise prediction intervals for period life-table death counts. The age distribution of death counts is an example of constrained data, which are nonnegative and have a constrained integral. A centered log-ratio transformation is used to remove the constraints. With a time series of unconstrained data, we introduce our bootstrap method to construct prediction intervals, thereby quantifying forecast uncertainty. The bootstrap method utilizes a dynamic factor model to capture both nonstationary and stationary patterns through a two-stage functional principal component analysis. To capture parameter uncertainty, the estimated principal component scores and model residuals are sampled with replacement. Using the age- and sex-specific life-table deaths for Australia and the United Kingdom, we study the empirical coverage probabilities and compare them with the nominal ones. The bootstrap method has superior interval forecast accuracy, especially for the one-step-ahead forecast horizon.