In this paper, we introduce covariate adjusted partially functional linear regression models, in which both the response and the covariates in the non-functional linear component can only be observed after being distorted by some multiplicative factors. We first estimate the distorting functions by nonparametrically regressing the response variables and covariates on the distorting covariate, and then the estimators of the slope function and the partially linear coefficient are obtained using the estimated response variables and covariates and functional principal component analysis based on corrected profile least-squares. We establish the asymptotic properties of the proposed estimators. In addition, using empirical likelihood and functional principal component analysis, we construct confidence intervals and bands for the coefficient parameters and the slope function, respectively. Finally, some simulation studies and an empirical analysis of a real dataset are conducted to illustrate the finite sample performance of the proposed method.

中文翻译：

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协变量调整部分函数线性回归模型的估计和推断

在本文中，我们引入了协变量调整部分函数线性回归模型，其中非函数线性分量中的响应和协变量只有在被一些乘法因子扭曲后才能观察到。我们首先通过对扭曲协变量的响应变量和协变量进行非参数回归来估计扭曲函数，然后使用估计的响应变量和协变量以及基于校正轮廓的函数主成分分析获得斜率函数和部分线性系数的估计量最小二乘法。我们建立了所提出的估计量的渐近特性。此外，使用经验似然和函数主成分分析，我们分别为系数参数和斜率函数构建置信区间和带。最后，对真实数据集进行了一些模拟研究和实证分析，以说明所提出方法的有限样本性能。