Truncated Linear Models for Functional Data
Peter Hall, Giles Hooker(Submitted on 30 Jun 2014)
A conventional linear model for functional data involves expressing a response variable Y in terms of the explanatory function X(t), via the model: Y=a+∫Ib(t)X(t)dt+error, where a is a scalar, b is an unknown function and I=[0,α] is a compact interval. However, in some problems the support of bor X, I1 say, is a proper and unknown subset of I, and is a quantity of particular practical interest. In this paper, motivated by a real-data example involving particulate emissions, we develop methods for estimating I1. We give particular emphasis to the case I1=[0,θ], where θ∈(0,α], and suggest two methods for estimating a, b and θ jointly; we introduce techniques for selecting tuning parameters; and we explore properties of our methodology using both simulation and the real-data example mentioned above. Additionally, we derive theoretical properties of the methodology, and discuss implications of the theory. Our theoretical arguments give particular emphasis to the problem of identifiability.
Subjects: Methodology (stat.ME)Cite as: arXiv:1406.7732 [stat.ME] (or arXiv:1406.7732v1 [stat.ME] for this version)