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FUNCTIONAL LINEAR REGRESSION THAT'S INTERPRETABLE
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DOI：10.1214/08-AOS641.png)
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摘要
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Regression models to relate a scalar Y to a functional predictor X(t) are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, beta(t), with Y related to X(t) through integral beta(t)X(t)dt. Regions where beta (t) not equal 0 correspond to places where there is a relationship between X (t) and Y. Alternatively, points where beta(t) = 0 indicate no relationship. Hence, for interpretation put-poses, it is desirable for a regression procedure to be capable of producing estimates of beta(t) thin are exactly zero over regions with no apparent relationship and have simple structures over the remaining regions. Unfortunately, most fitting procedures result in an estimate for beta(t) that is rarely exactly zero and has unnatural wiggles making the curve hard to interpret. In this article we introduce a new approach which uses variable selection ideas, applied to various derivatives of beta(t), to produce estimates that Lire both interpretable, flexible and accurate. We call Our method Functional Linear Regression That's Interpretable (FLiRTI) and demonstrate it on simulated and real-world data sets. In addition, non-asymptotic theoretical bounds on the estimation error are presented. The bounds provide strong theoretical motivation for our approach.
Keyword:
Interpretable regression
functional linear regression
Dantzig selector
lasso
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