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- W4300789694 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 $I=[0, alpha]$ 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 $I_1=[0,theta]$, where $theta in(0,alpha]$, and suggest two methods for estimating $a$, $b$ and $theta$ 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." @default.
- W4300789694 created "2022-10-04" @default.
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- W4300789694 date "2014-06-30" @default.
- W4300789694 modified "2023-09-25" @default.
- W4300789694 title "Truncated Linear Models for Functional Data" @default.
- W4300789694 doi "https://doi.org/10.48550/arxiv.1406.7732" @default.
- W4300789694 hasPublicationYear "2014" @default.
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