SPECIFICATION TEST FOR CONDITIONAL DISTRIBUTION WITH FUNCTIONAL DATA
构建了一个检验统计量，用于检验条件密度函数的特定形式，主要创新在于考虑函数型解释变量，并基于非参数函数型数据分析的最新进展构造统计量，研究了其渐近和有限样本性质。
In this paper we construct a statistic to test a specific form of the conditional density function. The main point of this work is to consider a functional explanatory variable, and the statistic is constructed following recent advances in nonparametric functional data analysis. The asymptotic behavior of the test statistic is studied under both the null hypothesis and some local alternative hypothesis. Then, the finite sample behavior of the method is studied through simulated examples. This paper is one of the first in the setting of nonparametric specification tests when functional data are involved.