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From Inspiration to Impact: Sir David Cox's Influence on My Research

Published onApr 27, 2023

From Inspiration to Impact: Sir David Cox's Influence on My Research

I was deeply saddened by the news that Sir David Cox passed away in January 2022. Although I only had the privilege of meeting him a few times during statistical conferences and speaking with him briefly on one or two occasions, his immense contributions to the field of statistics had a profound and lasting impact on my research. As a student, I was greatly impressed by the mathematical elegance and practical significance of the Cox proportional hazard model. The simultaneous pursuit of both mathematical beauty and practical utility has been a constant theme in Sir David Cox’s long and illustrious statistical research career, and has guided me to pursue research that has impacts in both statistical and the wider scientific communities.

Even in his late 90s, Sir David Cox was still producing top-class research and leading the field into new directions. In a series of articles, Battey and Cox explored the challenging problem of handling a large number of nuisance parameters in high-dimensional statistical analysis, and provided beautiful solutions for specialized contexts (Battey & Cox, 2020, 2022b,a; Battey et al., 2022). In statistical problems where the model is parametrized by an unknown high-dimensional parameter, it is a typical assumption in the literature that this high-dimensional parameter possesses some low-dimensional structure such as sparsity. However, in many applications, the model may depend on not just parameters of interest, which can be sparse, but also dense nuisance parameters. Inspired by Sir David’s research, I investigated the problem of two-sample testing of sparse differences in the regression coefficients of two high-dimensional linear models, which led to an interesting new procedure with surprising theoretical results quantifying the testing radius in this problem (Gao & Wang, 2022).

Tengyao Wang has no financial or non-financial disclosures to share for this article.

Battey, H., & Cox, D. (2020). High dimensional nuisance parameters: An example from parametric survival analysis. *Information Geometry*, *3*, 119–148.

Battey, H., & Cox, D. (2022a). Some aspects of non-standard multivariate analysis. *Journal of Multivariate Analysis*, *188*(C), Article 104810.

Battey, H., & Cox, D. (2022b). Some perspectives on inference in high dimensions. *Statistical Science*, *37*(1), 110–122.

Battey, H., Cox, D., & Lee, S. H. (2022). On partial likelihood and the construction of factorisable transformations. *Information Geometry*. https://doi.org/10.1007/s41884-022-00068-8

Gao, F., & Wang, T. (2022). Two-sample testing of high-dimensional linear regression coefficients via complementary sketching. *The Annals of Statistics*, *50*(5), 2950–2972.

©2023 Tengyao Wang. This article is licensed under a Creative Commons Attribution (CC BY 4.0) International license, except where otherwise indicated with respect to particular material included in the article.

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