论文标题
与一般不完美变量的加性回归
Additive regression with general imperfect variables
论文作者
论文摘要
在本文中，我们研究了一个加性模型，其中响应变量是希尔伯特空间值的，预测因子是多元欧几里得人，并且两者都可能不完美。考虑到希尔伯特空间值的响应，可以覆盖欧几里得，组成，功能和密度值变量。通过处理不完善的响应，我们可以覆盖在Riemannian歧管中采用值的功能变量，并且只有来自密度值值响应的随机样本可用的情况。该治疗方法也可以应用于半参数回归中。处理不完美的预测因子使我们能够涵盖从希尔伯特（Hilbert）空间值变量获得的各种主组件和奇异组分分数。为了估计具有此类变量的加性模型，我们使用平滑的背贴方法。我们提供回归估计量的完整非反应性和渐近性特性，并通过几项模拟研究和实际数据应用介绍其广泛的应用。
In this paper, we study an additive model where the response variable is Hilbert-space-valued and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows to cover Euclidean, compositional, functional and density-valued variables. By treating imperfect responses, we can cover functional variables taking values in a Riemannian manifold and the case where only a random sample from a density-valued response is available. This treatment can also be applied in semiparametric regression. Dealing with imperfect predictors allows us to cover various principal component and singular component scores obtained from Hilbert-space-valued variables. For the estimation of the additive model having such variables, we use the smooth backfitting method. We provide full non-asymptotic and asymptotic properties of our regression estimator and present its wide applications via several simulation studies and real data applications.
