In real data analysis, practitioners frequently come across the case that a discrete response will be related to both a function-valued random variable and a vector-value random variable as the predictor variables. In this paper, we consider the generalized functional partially linear models (GFPLM). The infinite slope function in the GFPLM is estimated by the principal component basis function approximations. Then, we consider the theoretical properties of the estimator obtained by maximizing the quasi likelihood function. The asymptotic normality of the estimator of the finite dimensional parameter and the rate of convergence of the estimator of the infinite dimensional slope function are established, respectively. We investigate the finite sample properties of the estimation procedure via Monte Carlo simulation studies and a real data analysis.

中文翻译：

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基于 FPCA 的广义函数部分线性模型估计

在实际数据分析中，从业者经常会遇到这样的情况，即离散响应将同时与函数值随机变量和向量值随机变量相关作为预测变量。在本文中，我们考虑广义函数部分线性模型（GFPLM）。GFPLM 中的无限斜率函数由主成分基函数近似值估计。然后，我们考虑通过最大化拟似然函数获得的估计量的理论性质。分别建立了有限维参数估计量的渐近正态性和无限维斜率函数估计量的收敛速度。我们通过蒙特卡罗模拟研究和真实数据分析来研究估计程序的有限样本特性。