函数型数据基展开的同质性检验问题及其在阻变存储器中的应用
Homogeneity problem for basis expansion of functional data with applications to resistive memories
AI总结：
针对函数型数据，提出基于基展开的参数与非参数同质性检验方法，解决非高斯RRAM电流/电压曲线的同质性检验问题，并应用于三种RRAM技术的重置曲线。
摘要：
本文针对函数型数据，研究了检验多于两个不同样本是否来自同一总体的同质性检验问题。该方法论结果源于对不同材料和有源层厚度制造的电子器件同质性研究的动机。当与每个样本相关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，并简化为检验组均值函数的相等性（FANOVA）。问题在于，与阻变随机存取存储器（RRAM）相关的电流/电压曲线并非由高斯过程生成，因此需要一种不同的方法来进行同质性检验。为解决此问题，提出了两种基于样本曲线基展开的参数和非参数方法。第一种方法是对样本曲线的基系数向量进行多元同质性检验。第二种方法基于利用样本曲线的函数型主成分分析（FPCA）进行降维，并对主成分得分向量进行多元同质性检验。采用不同的近似数值技术来调整实验数据以适应统计研究。进行了广泛的模拟研究，以分析这两种方法在参数和非参数情形下的性能。最后，将所提出的方法应用于三种不同RRAM技术中测量的三组实验重置曲线样本。
英文摘要：
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.
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