Resumen de Statistical inference on the significance of rows and columns for matrix-valued data in an additive model
Xiumin Liu, Lu Niu, Junlong Zhao
Matrix-valued data arise in many applications. In this paper, we consider the setting where one collects both a matrix-valued data and a generic scalar X that can be continuous, discrete or categorical. Since the rows and columns of often have specific meanings in practice, it is interesting to make statistical inferences on the significance of rows and columns of . In this paper, by taking into account the background effect, we propose a new measure on significance of rows and columns based on an additive model. The point estimates, hypothesis testings and confidence intervals of the significance of a given row or column of are considered. Moreover, a procedure is proposed to select significant rows and columns. Our method is applicable to both p and q being much larger than sample size n. Simulation results and real data analysis demonstrate the effectiveness of the proposed method.
