用嵌套组桥方法估计历史函数线性模型
Estimating Historical Functional Linear Models with a Nested Group Bridge Approach
摘要：
本文研究了一个标量-函数历史线性回归模型，该模型假设当时间超过某个截止点时，函数预测因子不影响响应。我们从局部稀疏建模的角度来处理这个问题，如果一个函数在其定义域的很大一部分上为零，则该函数是局部稀疏的。在历史线性模型中，斜率函数恰好是一个局部稀疏函数，在截止时间之后为零。然后，局部稀疏估计产生截止时间的估计。我们提出了一个嵌套的组桥惩罚，能够专门缩小一个函数的尾部。结合B样条基展开和惩罚最小二乘法，嵌套组桥方法可以识别截止时间，同时产生一个光滑的估计的斜率函数。所提出的局部稀疏估计被证明是一致的，而其数值性能的仿真研究所示。所提出的方法被证明与应用程序确定的影响，过去的发动机加速对当前的颗粒物排放。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
