OPERATIONAL TIME AND IN-SAMPLE DENSITY FORECASTING

• 成果类型: Article
• 署名作者: Lee, Young K.; Mammen, Enno; Nielsen, Jens P.; Park, Byeong U.
• 署名单位: Kangwon National University; Ruprecht Karls University Heidelberg; City St Georges, University of London; Seoul National University (SNU)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1486
• 发表日期: 2017
• 页码: 1312-1341
• 关键词: period-cohort model; chain-ladder; regression

摘要

In this paper, we consider a new structural model for in-sample density forecasting. In-sample density forecasting is to estimate a structured density on a region where data are observed and then reuse the estimated structured density on some region where data are not observed. Our structural assumption is that the density is a product of one-dimensional functions with one function sitting on the scale of a transformed space of observations. The transformation involves another unknown one-dimensional function, so that our model is formulated via a known smooth function of three underlying unknown one-dimensional functions. We present an innovative way of estimating the one-dimensional functions and show that all the estimators of the three components achieve the optimal one-dimensional rate of convergence. We illustrate how one can use our approach by analyzing a real dataset, and also verify the tractable finite sample performance of the method via a simulation study.