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

Xiumin Liu (), Lu Niu () and Junlong Zhao ()
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Xiumin Liu: Beijing Technology and Business University
Lu Niu: Beijing Jiaotong University
Junlong Zhao: Beijing Normal University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 3, No 1, 785-828

Abstract: Abstract 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.

Keywords: Matrix-valued data; Row and column significance; Hypothesis testing; Confidence interval; Variable screening; 62H12; 62H15; 62P10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-023-00852-3

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