Estimating Historical Functional Linear Models with a Nested Group Bridge Approach
arXiv:1809.05091
Abstract
We study a scalar-on-function historical 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 historical 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 locally sparse estimator is shown to be consistent, while its numerical performance is illustrated by simulation studies. The proposed method is demonstrated with an application of determining the effect of the past engine acceleration on the current particulate matter emission.
References in corpus (16)
- Rejoinder to "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Least Angle Regression
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Functional linear regression analysis for longitudinal data
- Prediction in functional linear regression
- A reproducing kernel Hilbert space approach to functional linear regression
- Functional linear regression that's interpretable
- Review of Functional Data Analysis
- A Smooth and Locally Sparse Estimator for Functional Linear Regression via Functional SCAD Penalty