Homogeneity problem for basis expansion of functional data with applications to resistive memories

Abstract

The homogeneity problem for testing if more than two different samples come from the same population is consideredfor the case of functional data. The methodological results are motivated by the study of homogeneity of electronic devicesfabricated by different materials and active layer thicknesses. In the case of normality distribution of the stochastic processesassociated with each sample, this problem is known as Functional ANOVA problem and is reduced to test the equality of themean group functions (FANOVA). The problem is that the current/voltage curves associated with Resistive Random AccessMemories (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 curvesare 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) andtesting multivariate homogeneity on a vector of principal components scores. Different approximation numerical techniques areemployed to adapt the experimental data for the statistical study. An extensive simulation study is developed for analyzing theperformance of both approaches in the parametric and non-parametric cases. Finally, the proposed methodologies are appliedon three samples of experimental reset curves measured in three different RRAM technologies.