The main ideas behind the classical multivariate logistic regression model make sense when translated to the functional setting, where the explanatory variable $X$ is a function and the response $Y$ is binary. However, some important technical issues appear (or are aggravated with respect to those of the multivariate case) due to the functional nature of the explanatory variable. First, the mere definition of the model can be questioned: while most approaches so far proposed rely on the $L_2$-based model, we suggest an alternative (in some sense, more general) approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS). The validity conditions of such RKHS-based model, as well as its relation with the $L_2$-based one are investigated and made explicit in two formal results. Some relevant particular cases are considered as well. Second we show that, under very general conditions, the maximum likelihood (ML) of the logistic model parameters fail to exist in the functional case. Third, on a more positive side, we suggest an RKHS-based restricted version of the ML estimator. This is a methodological paper, aimed at a better understanding of the functional logistic model, rather than focusing on numerical and practical issues.

翻译：典型的多变后勤回归模式背后的主要思想在转换成功能环境时是有道理的,因为解释性可变美元是一个函数,而对美元的反应是二元。然而,由于解释性可变因素的功能性质,出现了一些重要的技术问题(或因多变情况而更加严重)。首先,该模式的简单定义可以受到质疑:虽然迄今为止提出的大多数方法都依赖以美元为基的2美元模式,但我们建议一种替代(某种意义上的,更一般的)方法,基于再生产Kernel Hilbert空间理论(RKHS),这种基于RKHS的模型的有效性条件及其与以美元为基数的2美元模式的关系受到调查,并在两个正式结果中加以明确阐述。一些相关的特定案例也得到了考虑。第二,我们表明,在非常一般的条件下,后勤模式参数的最大可能性(ML)在功能案件中是存在的。第三,在更积极的方面,我们建议基于RKHSS的限制性版本。这是一份方法文件,其与以更实际的物流问题为重点,而不是以更精确的模型为重点。