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June 2017 Operational time and in-sample density forecasting
Young K. Lee, Enno Mammen, Jens P. Nielsen, Byeong U. Park
Ann. Statist. 45(3): 1312-1341 (June 2017). DOI: 10.1214/16-AOS1486

Abstract

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.

Citation

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Young K. Lee. Enno Mammen. Jens P. Nielsen. Byeong U. Park. "Operational time and in-sample density forecasting." Ann. Statist. 45 (3) 1312 - 1341, June 2017. https://doi.org/10.1214/16-AOS1486

Information

Received: 1 July 2015; Revised: 1 June 2016; Published: June 2017
First available in Project Euclid: 13 June 2017

zbMATH: 1371.62031
MathSciNet: MR3662456
Digital Object Identifier: 10.1214/16-AOS1486

Subjects:
Primary: 62G07
Secondary: 62G20

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

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 3 • June 2017
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