Australian & New Zealand Journal of Statistics最新文献

We present a normalising transformation of the Hill estimator to improve the convergence rate in finite-sample performance. Our proposal for the normalising transformation is based on the higher order asymptotic expansion of the Hill estimator. The transformation is automatic and simple in computation. The resulting transformation theoretically improves the approximation to the standard normal distribution, achieving a lower error rate compared with the variance stabilisation or the Wilson and Hilferty approximation. The numerical results of simulations also align with our theoretical findings.

Clem Pratt was born in Brisbane in 1936 and died in Melbourne in 2025, aged 88 years. He is survived by his three children, grandchildren and great-grandchildren. He was President of the Statistical Society of Australia (SSA) from 1969 to 1971.

Clem was educated in Brisbane and was dux of Brisbane High School in 1954. At the age of 18, he enrolled in engineering studies at the University of Queensland, and then pursued postgraduate studies there and at the University of London, being awarded the degrees of BSc (Qld), BEng (Hons) (Qld), MEngSc (Qld) and PhD (London).

His background was primarily in queueing and congestion theory but also operations research more generally. He studied for his PhD (1961–1963) at Birkbeck College, University of London, under the direction of Professor (later Sir) David Cox; the topic for his dissertation was ‘Congestion Problems In Automatic And Semi-automatic Telephone Exchanges’.

In the 1960s, as an external part-time lecturer, he taught ‘Statistical Methods for Research Workers’ and ‘Operations Research’ at Melbourne University as part of the third-year Statistics course. I was fortunate to be one of his students and found his lectures inspiring. It was an early experience of the practical use of statistical theory.

Pratt helped set up the Victorian Branch of the SSA and was an early President of the Branch; it was during his tenure as President that the annual Belz Lecture was established in 1969. There were only three Branches of the SSA at that time (initially NSW, followed by Canberra and then Victoria).

Pratt had a 38-year career with Telstra (previously the PMG and then Telecom Australia), initially specialising in telephone traffic engineering, and later working in information systems planning and development, network operations, quality management and network planning. During this period, he represented Australia on several international bodies (including the International Telecommunication Union in Geneva and the Economic Commission for Asia & the Far East in Bangkok) and was on the governing body of the International Teletraffic Congresses. He also chaired the Board at the Teletraffic Research Centre at the University of Adelaide in the late 1990s. The Centre, incorporating the Centre for Defence Communications and Information Networks, conducted research and development for both the commercial and defence sectors.

In retirement, he lived in Melbourne where he enjoyed music, theatre, amateur astronomy and the company of his grandchildren and great-grandchildren. He became non-verbal in the latter years of his life because of a throat surgery but I was fortunate to have several email exchanges with him in late 2023 as part of my research for the SSA History Standing Committee.

Datasets for statistical analysis become extremely large even when stored on one single machine with some difficulty. Even when the data can be stored in one machine, the computational cost would still be intimidating. We propose a divide and conquer solution to density estimation using Bayesian mixture modelling, including the infinite mixture case. The methodology can be generalised to other application problems where a Bayesian mixture model is adopted. The proposed prior on each machine or subgroup modifies the original prior on both mixing probabilities and the rest of parameters in the distributions being mixed. The ultimate estimator is obtained by taking the average of the posterior samples corresponding to the proposed prior on each subset. Despite the tremendous reduction in time thanks to data splitting, the posterior contraction rate of the proposed estimator stays the same (up to a $��\log �$ factor) as that using the original prior when the data is analysed as a whole. Simulation studies also justify the competency of the proposed method compared to the established WASP estimator in the finite-dimension case. In addition, one of our simulations is performed in a shape-constrained deconvolution context and reveals promising results. The application to a GWAS dataset reveals the advantage over a naive divide and conquer method that uses the original prior.

Networks are mathematical structures that allow the representation of complex systems by jointly modelling the elements of the system and the relationships that exist among them. To analyse different contexts or systems, methodological tools are necessary to allow for the quantitative estimation of the differences existing between two or more networks. For this purpose, various tools have been proposed in the literature. This study is an exploratory analysis of the impacts that different methods (distances and spectral methods) have on the comparative evaluation of two networks. The analyses were conducted through a simulation study that considered three different perturbation schemes to investigate the behaviour of each method with increasing randomness in the perturbation scheme (i.e., edge removal). Results show that the distances between adjacency matrices are sensitive only to changes in the network density, while spectral methods are sensitive to changes in both the network density and the degree of the nodes.

We investigate the use of multiple linked lists for population size estimation and to estimate the relationships between covariates appearing on the lists. Over the lists, the covariates aim to measure the same concept. The relationships between the covariates are not fully known because of missing values on the covariates: some cases do not appear in some lists; some cases are on one or more of the lists but have missing covariate values on some of the lists; and some cases are not observed in any list. In earlier work, multiple system estimation has been combined with latent class analysis to give a consensus estimate where an underlying dichotomous categorical covariate is measured differently in different lists. This was applied to ethnicity covariates in New Zealand with two levels, Māori and non-Māori. In this paper, we apply this approach to ethnicity covariates with a larger number of categories, and find that it produces satisfactory results with four categories. We assess the purity of the latent classes using entropy and conditional probability measures. We also examine the evolution of annual estimates from multiple lists (where one list is the population census) over 2013–2020, finding that the estimated latent class proportions are very stable. We assess the impact of disclosure control measures on the outputs.

Fused lasso regression is a popular method for identifying homogeneous groups and sparsity patterns in regression coefficients based on either the presumed order or a more general graph structure of the covariates. However, the traditional fused lasso may yield misleading outcomes in the presence of outliers. In this paper, we propose an extension of the fused lasso, namely the robust adaptive fused lasso (RAFL), which pursues homogeneity and sparsity patterns in regression coefficients while accounting for potential outliers within the data. By using Huber's loss or Tukey's biweight loss, RAFL can resist outliers in the responses or in both the responses and the covariates. We also demonstrate that when the adaptive weights are properly chosen, the proposed RAFL achieves consistency in variable selection, consistency in grouping and asymptotic normality. Furthermore, a novel optimization algorithm, which employs the alternating direction method of multipliers, embedded with an accelerated proximal gradient algorithm, is developed to solve RAFL efficiently. Our simulation study shows that RAFL offers substantial improvements in terms of both grouping accuracy and prediction accuracy compared with the fused lasso, particularly when dealing with contaminated data. Additionally, a real analysis of cookie data demonstrates the effectiveness of RAFL.