2025-08-27Recently, the research team led by Professor Pang Shanqi from the School of Mathematics and Statistics of our university made a significant breakthrough in the construction of nested orthogonal arrays, particularly mixed-level nested orthogonal arrays. The related result, titled Construction of Asymmetric Nested Orthogonal Array, was published in the international statistics journal Journal of the American Statistical Association (JASA). Professor Pang Shanqi is the first author, and the co-authors include Lin Xiao, a 2021 PhD student from our university’s School of Mathematics and Statistics; Professor Ai Mingyao of Peking University (the corresponding author); and Professor Peter Chien from the University of Wisconsin-Madison. Henan Normal University is the first credited unit.
A nested orthogonal array is a special type of orthogonal array consisting of a pair where a smaller array is nested within a larger one, and it is widely used in computer experiments and statistics. The paper proposes several general construction methods to create a series of asymmetric nested orthogonal arrays with flexible run sizes, numbers of levels, and strengths, enabling both the large and small arrays to achieve the maximum number of factors at the minimum run size. As a supplement to the concept of saturation in orthogonal arrays, the paper introduces a new concept of “flawlessness.” It classifies nested orthogonal arrays into nine types based on the saturation and flawlessness of the large and small arrays, and successfully constructs seven new types of these nested orthogonal arrays. The article not only details the most comprehensive collection of newly generated small and medium-sized nested orthogonal arrays, including optimized ones, but also lists their corresponding matrix forms. This provides a powerful tool for both theoretical researchers and practical users. The work not only offers valuable experience for constructing other special orthogonal arrays but also opens broader prospects for the application of orthogonal arrays in fields such as statistics, cryptography, coding, and quantum information.
This research in the field of statistical experimental design spanned four years and was funded by projects such as the National Natural Science Foundation of China. This is also another significant achievement from the research group following their publications in a Nature sub-journal on quantum information theory in 2019 and in the international statistics journal Annals of Statistics in 2021. Their previous work in Annals of Statistics on the construction of high-strength orthogonal arrays laid a solid foundation for this current research.
It is reported that Journal of the American Statistical Association is the flagship journal of the American Statistical Association (ASA) (founded in 1888). The journal is consistently dedicated to groundbreaking innovations in statistical theory and computational methods and promotes their paradigm-shifting applications in data science practice. The journal is renowned for its dual standards of mathematical rigor and its focus on solving complex real-world problems, covering frontier fields from basic statistical inference to high-dimensional computation. It places special emphasis on work that brings methodological innovations to interdisciplinary research. JASA is known as one of the top four journals in statistics, publishing only around 150 papers per year.
Paper link: https://doi.org/10.1080/01621459.2025.2555058
(School of Mathematics and Statistics, Wang Jing)
