Asymptotics for in-sample density forecasting
样本内密度预测的渐近理论AI 解读 ↓
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样本内密度预测的渐近理论
- 研究问题
- 当密度仅在部分区域可观测时，如何依靠结构限制预测未观测区域，并容纳观测时间分解和乘法季节效应？
- 方法与思路
- 作者假设密度为一维函数的乘积，利用该结构进行外推，并提出基于回代拟合的平滑估计，同时纳入季节因子。
- 材料陈述的贡献
- 摘要称推广已有密度预测模型并建立完整渐近理论，提供保险报案年度内预算示例和支持理论的小样本研究。
- 阅读关注点
- 阅读全文时应核对乘法结构如何保证外推识别、观测区域的限制、季节因子的处理，以及回代拟合估计的渐近条件。
- 阅读边界
- 材料为稿件版本未注明的 OpenAlex 索引摘要；精确外推依赖所设结构，摘要未列出识别和渐近条件，不能判断结构误设时的表现。
原文摘要
This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed. Identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation. In this paper, the structural assumption is made that the density is a product of one-dimensional functions. The theory is quite general in assuming the shape of the region where the density is observed. Such models naturally arise when the time point of an observation can be written as the sum of two terms (e.g., onset and incubation period of a disease). The developed theory also allows for a multiplicative factor of seasonal effects. Seasonal effects are present in many actuarial, biostatistical, econometric and statistical studies. Smoothing estimators are proposed that are based on backfitting. Full asymptotic theory is derived for them. A practical example from the insurance business is given producing a within year budget of reported insurance claims. A small sample study supports the theoretical results.