期刊
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
卷 78, 期 3, 页码 637-653出版社
WILEY
DOI: 10.1111/rssb.12125
关键词
Consistency; Functionally equivalent models; Identifiability; Mean-squared prediction error; Regression; Slope function; Statistical smoothing; Support interval
资金
- Australian Research Council
- National Science Foundation [DMS-1053252, DEB-1353039]
- Direct For Mathematical & Physical Scien [1301377] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1301377] Funding Source: National Science Foundation
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+integral(I)b(t) X(t)dt + 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. 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 is an element of(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 by 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.
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