ABSTRACT Orthogonalized residuals identify model misspecification in sparse contingency tables and latent variable models. While many orthogonalization methods exist, the structural reasons for their different diagnostic behaviors remain unclear. This paper formalizes a diagnostic trilemma based on three desirable properties: sequential innovation orthogonality, localized interpretability and permutation invariance. We argue these objectives cannot generally be achieved simultaneously for correlated residuals. Triangular decompositions, including sequential sums of squares, QR, Cholesky and Helmert methods, maintain sequential innovation orthogonality and localized interpretability but lack permutation invariance. Spectral methods maintain permutation invariance but lack localized interpretability. Polar decompositions retain partial localization but fail to provide the sequential structures needed for innovation‐based diagnostics. The proposed framework clarifies the strengths and limitations of existing orthogonalization methods and helps explain why triangular decompositions are often preferred for directional diagnostics.
ABSTRACT Statisticians commonly find themselves working in isolation, with some managed exclusively by nonstatisticians. Mentoring is critical to help statisticians build their careers and network. We created a national mentoring program to support statisticians across Australia through the national professional statistical organisation: the Statistical Society of Australia. This national mentoring program is now in its sixth year, including the pilot, and is well established in the Society. In this article, we describe why and how this program was created, outlining some of our challenges and how the program has evolved. We provide advice for others interested in creating a mentoring program for statisticians.
ABSTRACT Autocorrelated bivariate count data frequently arise in criminal, environmental and financial studies, where capturing both serial dependence and cross‐series interaction is essential for statistical modelling and inference. In many applications, such dynamics are further influenced by exogenous covariates such as policy interventions or environmental factors, leading to time‐varying dependence structures that are not adequately captured by standard models. Existing bivariate integer‐valued autoregressive (BINAR) models mainly rely on constant or observation‐driven coefficients and rarely incorporate covariate information, which restricts their ability to represent evolving dependence in multivariate count processes. To address this limitation, we propose a covariate‐driven doubly stochastic bivariate integer‐valued autoregressive process, in which the thinning mechanism evolves jointly with past observations and exogenous covariates. This formulation extends the classical BINAR framework by allowing the dependence structure to vary dynamically under both internal and external driving mechanisms. The basic statistical properties of the proposed process are derived, and two estimation methods are developed, including an EM‐based algorithm. Monte Carlo simulations and a real data application are conducted to assess finite‐sample performance and robustness under different settings.
ABSTRACT This paper studies variance estimation in difference‐in‐differences (DID) designs under covariate matching. While matching is widely used to improve covariate balance, it induces a dependence structure that complicates variance estimation. In particular, covariate‐based matching generates positive correlation within matched pairs, which reduces the variance of the DID estimator. Standard variance estimators fail to account for this design‐induced covariance and therefore yield systematically conservative standard errors. We characterize the asymptotic variance implied by the matched design and propose a projection‐based variance estimator to remove variation attributable to the matching covariates. Simulation results show that the proposed estimator achieves accurate coverage, whereas standard methods substantially overestimate uncertainty. An empirical application illustrates the practical implications for inference.
ABSTRACT Basis precision matrix plays fundamental roles in the study of compositional data. Constrained and unconstrained optimization methods are usually used to estimate basis precision matrices. Zhang and He (2019) discuss that problem by an unconstrained optimization estimator. However, the authors do not give any convergence rates. Zhang et al. (2025) define their constrained optimization estimator and provide a convergence rate. In this paper, we extend Zhang and He's work. It turns out that our unconstrained ‐regularized estimator attains the same convergence rate as the one of Zhang et al. Moreover, our estimator outperforms Zhang et al.'s for numerical experiments.
