The homogeneity problem for testing if more than two different samples come from the same population is considered for the case of functional data. The methodological results are motivated by the study of homogeneity of electronic devices fabricated by different materials and active layer thicknesses. In the case of normality distribution of the stochastic processes associated with each sample, this problem is known as Functional ANOVA problem and is reduced to test the equality of the mean group functions (FANOVA). The problem is that the current/voltage curves associated with Resistive Random Access Memories (RRAM) are not generated by a Gaussian process so that a different approach is necessary for testing homogeneity. To solve this problem two different parametric and nonparametric approaches based on basis expansion of the sample curves are proposed. The first consists of testing multivariate homogeneity tests on a vector of basis coefficients of the sample curves. The second is based on dimension reduction by using functional principal component analysis of the sample curves (FPCA) and testing multivariate homogeneity on a vector of principal components scores. Different approximation numerical techniques are employed to adapt the experimental data for the statistical study. An extensive simulation study is developed for analyzing the performance of both approaches in the parametric and non-parametric cases. Finally, the proposed methodologies are applied on three samples of experimental reset curves measured in three different RRAM technologies.

翻译：本文考虑函数型数据背景下，检验两个以上不同样本是否来自同一总体（同质性检验）的问题。该方法论研究源于对采用不同材料和有源层厚度制备的电子器件同质性的探讨。当各样本对应的随机过程服从正态分布时，该问题被称为函数型方差分析问题，可简化为检验均值函数组的相等性（FANOVA）。然而，由于阻变存储器（RRAM）的电流/电压曲线并非由高斯过程生成，需要采用不同方法进行同质性检验。为解决此问题，本文提出两种基于样本曲线基展开的参数与非参数方法：第一种方法对样本曲线基系数向量进行多元同质性检验；第二种方法通过函数型主成分分析（FPCA）对样本曲线降维，并对主成分得分向量进行多元同质性检验。研究中采用多种近似数值技术使实验数据适应统计分析要求。通过大量仿真研究，分析了两种方法在参数与非参数情形下的性能。最后，将所提方法应用于三种不同RRAM技术实测的复位曲线样本中。