Abstract

We addressed the problem of estimating regression coefficients for partially linear models, where the nonparametric component is approximated using smoothing splines and subspace information is available. We proposed pretest and shrinkage estimation strategies using the profile likelihood estimator as the benchmark. We examined the asymptotic distributional bias and risk of the proposed estimators, and assessed their relative performance with respect to the unrestricted profile likelihood estimator under varying degrees of uncertainty in the subspace information. The shrinkage-based estimators uniformly dominated the unrestricted profile likelihood estimator. The positive-part shrinkage estimator was shown to be more efficient than the others, and was robust against uncertain subspace information. We also compared the performance of penalty estimators with those of the proposed estimators via a Monte Carlo simulation, and found that the proposed estimators were more efficient. The proposed estimation strategies were applied to a real dataset to evaluate their practical usefulness. The results were consistent with those from theory and simulation.

摘要

我们解决了估计部分线性模型的回归系数的问题，其中非参数分量使用平滑样条曲线进行近似，并且子空间信息可用。我们提出了使用轮廓似然估计器作为基准的预测试和收缩估计策略。我们检查了所提出的估计量的渐近分布偏差和风险，并评估了它们在子空间信息中不同程度的不确定性下相对于无限制轮廓似然估计量的相对性能。基于收缩的估计器一致地支配了无限制的轮廓似然估计器。正部分收缩估计器被证明比其他方法更有效，并且对不确定的子空间信息具有鲁棒性。我们还通过蒙特卡罗模拟比较了惩罚估计器与提议估计器的性能，发现提议的估计器更有效。将所提出的估计策略应用于真实数据集以评估其实际用途。结果与理论和模拟结果一致。