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April 2015 Asymptotics for in-sample density forecasting
Young K. Lee, Enno Mammen, Jens P. Nielsen, Byeong U. Park
Ann. Statist. 43(2): 620-651 (April 2015). DOI: 10.1214/14-AOS1288

Abstract

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.

Citation

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Young K. Lee. Enno Mammen. Jens P. Nielsen. Byeong U. Park. "Asymptotics for in-sample density forecasting." Ann. Statist. 43 (2) 620 - 651, April 2015. https://doi.org/10.1214/14-AOS1288

Information

Published: April 2015
First available in Project Euclid: 3 March 2015

zbMATH: 1312.62050
MathSciNet: MR3319138
Digital Object Identifier: 10.1214/14-AOS1288

Subjects:
Primary: 62G07 , 62G20

Keywords: backfitting , chain ladder , Density estimation , kernel smoothing

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 2 • April 2015
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