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Estimating Truncated Functional Linear Models With a Nested Group Bridge Approach

We study a scalar-on-function truncated linear regression model which assumes that the functional predictor does not influence the response when the time passes a certain cutoff point. We approach this problem from the perspective of locally sparse modeling, where a function is locally sparse if it is zero on a substantial portion of its defining domain. In the truncated linear model, the slope function is exactly a locally sparse function that is zero beyond the cutoff time. A locally sparse estimate then gives rise to an estimate of the cutoff time. We propose a nested group bridge penalty that is able to specifically shrink the tail of a function. Combined with the B-spline basis expansion and penalized least squares, the nested group bridge approach can identify the cutoff time and produce a smooth estimate of the slope function simultaneously. The proposed nested group bridge estimator is shown to be consistent, while its numerical performance is illustrated by simulation studies. The proposed nested group bridge method is demonstrated with an application of determining the effect of the past engine acceleration on the current particulate matter emission. Supplementary materials for this article are available online.

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Informasi Detail

Judul Seri

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS; Vol.29 No.3 September 2020

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 620 - 628

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

-

Edisi

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Subjek

FUNCTIONAL DATA ANALYSIS
FUNCTIONAL LINEAR REGRESSION
PENALIZED B-SPLINES
B-SPLINE BASIS FUNCTIONS
GROUP BRIDGE APPROACH
LOCALLY SPARSE

Info Detail Spesifik

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Pernyataan Tanggungjawab

Tianyu Guan, Zhenhua Lin, Jiguo Cao

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