We are delighted to present a special issue of The Canadian Journal of Statistics (CJS) in honour of Professor Nancy Reid. The articles in this collection have been contributed by a group of participants who attended a workshop entitled “Statistics at its Best” in Toronto on 5 May 2022. The workshop was organized by the Department of Statistical Sciences at the University of Toronto to celebrate Professor Reid’s 70th birthday. It highlighted her remarkable contributions to Statistical Science and her dedication to the profession, exemplified in research, leadership, service and education of the next generation of statisticians. Professor Reid’s impactful career has played a crucial role in fostering the growth of the Canadian statistical community. This workshop was part of a series of celebratory activities coordinated by the Statistical Society of Canada, marking the 50th anniversary of the statistical community in this country.

This collection of articles encompasses a wide range of topics. First, the engaging dialogue A conversation with Nancy Reid by Craiu and Yi sheds light on Professor Reid’s intellectual journey and perspectives on statistical science and data science.

In The inducement of population sparsity (Open Access), Battey presents the pioneering work on parameter orthogonalization by Cox and Reid as an inducement of abstract population-level sparsity. The article focuses on three important examples related to sparsity-inducing parameterizations or data transformations: covariance models, nuisance parameter elimination and high-dimensional regression. Strategies for inducing sparsity vary depending on the context and may involve solving partial differential equations or specifying parameterized paths. Battey concludes by presenting some open problems.

McCullagh then highlights, in A tale of two variances, the ambiguity and potential misinterpretation of the standard repeated-sampling concept of the variance in a finite-dimensional parametric model. He presents three operational interpretations, all numerically distinct and compatible with repeated sampling from a fixed parameter population. These interpretations help resolve contradictions between Fisherian variance and inverse-information variance.

We next turn to hypothesis testing for parameters on the boundary of their domain. In Improved inference for a boundary parameter (Open Access), Elkantassi, Bellio, Brazzale and Davison review theoretical work on the problem, including hard and soft boundaries, and iceberg estimators. They highlight the significant underestimation of the probability due to the limiting results, propose remedies based on the normal approximation for the profile score function, and outline the success of higher order approximations. Using these approaches, the authors develop an accurate test to assess the need for a spline component in a linear mixed model.

In Sparse estimation within Pearson’s system, with an application to financial market risk (Open Access), Carey, Genest and Ramsay tackle the challenging task of estimating a density within Pearson’s system, a class of models encompassing many classical univariate distributions. The authors propose an effective method by combining penalized regression and profiled estimation techniques. Through simulations and an application using S&P 500 data, they demonstrate that the method improves market risk assessment substantially, outperforming the value-at-risk and expected shortfall estimates currently used by financial institutions and regulators.

Urban, Bong, Orellana and Kass explore Oscillating neural circuits: Phase, amplitude, and the complex normal distribution (Open Access).They consider multiple oscillating time series in the frequency domain and discuss the complex-valued correlation, its similarities to real-valued Pearson correlation and dependence among oscillating series using the multivariate complex normal distribution. They introduce a complex latent variable model for narrow band-pass filtered signals, showing that the maximum likelihood estimate produces a latent coherence equivalent to the magnitude of complex canonical correlation. Applied to brain science data, the framework provides valuable insights.

Next, McCormack and Hoff consider the problem of low power in standard F-tests for group-specific linear hypotheses in multigroup data with small within-group sample sizes. In their article Tests of linear hypotheses using indirect information, they derive alternative test statistics, leveraging information sharing across groups. These group-specific tests offer, potentially, much higher power than the standard F-test, while maintaining the desired type I error rate. The tests use statistics optimized for marginal power based on a prior distribution that is derived from other groups’ data. Empirical studies demonstrate the superiority of the proposed tests over F-tests in terms of power and P-values.

Pace, Salvan and Sartori investigate Confidence sequences with composite likelihoods (Open Access). They examine confidence sequences in parametric statistical models based on likelihood ratios. They use simulations to assess the replicability properties of two types of confidence sequences: Robbins’ mixture confidence sequences and the running maximum likelihood confidence sequences of Wasserman, Ramdas and Balakrishnan. They also extend the use of mixture confidence sequences to pseudo-likelihoods, particularly composite likelihood.

Finally, Kalbfleisch and Xu explore rerandomization and optimal matching in observational studies. In Rerandomization and optimal matching (Open Access), they address the issue of chance imbalances in treatment groups, which are common in applications, especially in cluster randomized trials with relatively few and highly heterogeneous clusters. To compare two or more treatments, they propose a new design that outperforms existing options in terms of efficiency, as demonstrated through theoretical and empirical evaluations.

We hope that this collection of articles will not only serve as a fitting tribute to Professor Reid but also inspire researchers, practitioners and students to continue pushing the boundaries of statistical research and to make their own important contributions to the discipline.

We express our heartfelt gratitude to the contributors of the articles featured in this special issue. Their work illustrates the spirit of innovation that Professor Reid has instilled within our community. We would also like to extend our sincere thanks to the referees who offered their time and expertise to assess the articles. We are grateful to Johanna Nešlehová (CJS Editor) and Fang Yao (former CJS Editor) for their strong support in making this issue possible, with help from their assistant Julie Falkner.

Happy 70th birthday, Nancy, and congratulations on your remarkable career!

Guest Co-Editors

Grace Y. Yi

University of Western Ontario, Canada

Radu Craiu