Year: 2014
Type: preprint
Abstract: A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\int_I b(t)X(t)dt+\hbox{error}$, 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 $b$ or $X$, $I_1$ 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 $I_1$. We give particular emphasis to the case $I_1=[0,θ]$, where $θ\in(0,α]$, 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.
Source: arXiv (Cornell University)
Authors: Hall, Peter, Hooker, Giles
Institutions: The University of Melbourne, Cornell University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949951892