Speaker: 周永道，南开大学

Inviter: 熊世峰

Title: Experimental designs with functional and scalar inputs

Language: Chinese

Time & Venue: 2025.11.30 10:30-11:00 腾讯会议：971-892-074

Abstract: Many real-world manufacturing applications involve experiments with curved or functional inputs. The continuity of functional inputs results in the traditional methods for designs of experiments being unavailable, and existing researches with such inputs often focus on algorithms but lack the theoretical support. This paper establishes a theoretical framework for designs with scalar and functional inputs. For linear models, using B-spline expansion approach, we obtain the theoretical functional boundary and hence an explicit D-optimal design. In a model-freesetting, we first study a single functional input: two necessary conditions are shown to characterize the row and column structure of the coefficient matrix corresponding to space-filling functions, from which we derive an upper bound for functional separation distance. For mixed inputs, we establish an upper bound for the separation distance and, guided by this result, we develop a mapping algorithm based on scalar L2 maximin distance design which produces designs that nearly attain the bound. Furthermore, we theoretically reveal that, unlike scalar variables, space-filling property for functional inputs may conflict with functional part uncorrelated parameter estimation. To address this issue, for practical screening settings with mixed inputs, we introduce a novel design called mixed nearly orthogonal Latin hypercube design. Numerical studies demonstrate that the proposed designs outperform those obtained by existing algorithms and remain effective under respective model specifications.