Statistical inference on the significance of rows and columns for matrix-valued data in an additive model

Matrix-valued data arise in many applications. In this paper, we consider the setting where one collects both a matrix-valued data $$\textbf{Y}\in \mathbb {R}^{p\times q}$$ Y ∈ R p × q and a generic scalar X that can be continuous, discrete or categorical. Since the rows and columns of $$\textbf{Y}$$ Y often have specific meanings in practice, it is interesting to make statistical inferences on the significance of rows and columns of $$\textbf{Y}$$ Y . 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 $$\textbf{Y}$$ Y 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.