黎曼流形上的部分线性模型
Partially linear models on Riemannian manifolds
摘要：
在部分线性模型中，响应y对（x^T，t）的依赖性通过关系y= \x^T β+g（t）+ε建模，其中ε与（x^T，t）无关。本文在解释变量t取值于黎曼流形上时，构造了β和g的估计.我们的建议结合了这些模型的灵活性与一组解释变量的复结构。在适当的条件下，我们证明了β的估计是渐近正态的.通过模拟研究，我们探讨了性能的估计。最后，我们将所研究的模型应用于一个基于真实数据集的实例。
英文摘要：
In partially linear models the dependence of the response y on (x^T,t) is modeled through the relationship y=\x^T β+g(t)+ε where εis independent of (x^T,t). In this paper, estimators of βand g are constructed when the explanatory variables t take values on a Riemannian manifold. Our proposal combine the flexibility of these models with the complex structure of a set of explanatory variables. We prove that the resulting estimator of βis asymptotically normal under the suitable conditions. Through a simulation study, we explored the performance of the estimators. Finally, we applied the studied model to an example based on real dataset.
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