We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of functional covariates with constant regression parameters. In this paper, we present an alternative solution by employing the quadratic inference approach, a well-established method for analyzing correlated data, to estimate the regression coefficients. Our approach leverages non-parametrically estimated basis functions, eliminating the need for choosing working correlation structures. Furthermore, we demonstrate that our method achieves a parametric $\sqrt{n}$-convergence rate, contingent on an appropriate choice of bandwidth. This convergence is observed when the number of repeated measurements per trajectory exceeds a certain threshold, specifically, when it surpasses $n^{a_{0}}$, with $n$ representing the number of trajectories. Additionally, we establish the asymptotic normality of the resulting estimator. The performance of the proposed method is compared with that of existing methods through extensive simulation studies, where our proposed method outperforms. Real data analysis is also conducted to demonstrate the proposed method.

翻译：本文针对具有稠密函数型响应的常数线性效应模型中的估计问题展开研究。在此框架下，响应曲线的条件期望由函数型协变量的线性组合表示，且回归参数为常数。本文提出了一种替代解决方案，即采用二次推断方法——一种分析相关数据的成熟方法——来估计回归系数。我们的方法利用了非参数估计的基函数，从而无需选择工作相关结构。此外，我们证明，在适当选择带宽的条件下，我们的方法能够达到参数性的 $\sqrt{n}$ 收敛速度。当每条轨迹的重复测量次数超过某个阈值（具体而言，当超过 $n^{a_{0}}$，其中 $n$ 表示轨迹数量）时，即可观察到这种收敛性。此外，我们还建立了所得估计量的渐近正态性。通过大量的模拟研究，将所提方法的性能与现有方法进行了比较，结果表明我们的方法表现更优。同时，我们也进行了实际数据分析以验证所提方法的有效性。