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通过信号压缩进行函数对函数线性回归AI 解读

We consider functional linear regression models with a functional response and multiple functional predictors, with the goal of finding the best finite-dimensional approximation to the signal part of the response function. Defining the integrated squared correlation coefficient between a random variable and a random function, we propose to solve a penalized generalized functional eigenvalue problem, whose solutions satisfy that projections on the original predictors generate…

常微分方程参数广义剖面估计的渐近效率与有限样本性质AI 解读

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop efficient estimation procedures for these parameters. Among the proposed methods in the literature, the generalized profiling estimation method developed by Ramsay and colleagues is particularly promising for its computational efficiency and good…