Australian & New Zealand Journal of Statistics最新文献

{"title":"Matrix Healy Plot: A Practical Tool for Visual Assessment of Matrix-Variate Normality","authors":"Fen Jiang,&nbsp;Jianhua Zhao,&nbsp;Changchun Shang,&nbsp;Xuan Ma,&nbsp;Yue Wang,&nbsp;Ye Tao","doi":"10.1111/anzs.70068","DOIUrl":"https://doi.org/10.1111/anzs.70068","url":null,"abstract":"<div>\u0000 \u0000 <p>Matrix-valued data, where each observation is represented as a matrix, frequently arises in various scientific disciplines. Modelling such data often relies on matrix-variate normal distributions, making matrix-variate normality testing crucial for valid statistical inference. Recently, the Distance-Distance (DD) plot has been introduced as a graphical tool for visually assessing matrix-variate normality. However, the Mahalanobis-squared distances (MSD) used in the DD plot require vectorizing matrix observations, restricting its applicability to cases where the dimension of the vectorized data does not exceed the sample size. To address this limitation, we propose a novel graphical method called the Matrix Healy (MatHealy) plot, an extension of the Healy plot for vector-valued data. This new plot is based on matrix-based MSD that leverages the inherent structure of matrix data. Consequently, it offers a more reliable visual assessment. Importantly, the MatHealy plot eliminates the sample size restriction of the DD plot and hence more applicable to matrix-valued data. Empirical results demonstrate its effectiveness and practicality compared to the DD plot across various scenarios, particularly in cases where the DD plot is not available due to limited sample sizes.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 4","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Malcolm Paul Quine, 1945–2026","authors":"Eugene Seneta,&nbsp;Neville Weber","doi":"10.1111/anzs.70067","DOIUrl":"https://doi.org/10.1111/anzs.70067","url":null,"abstract":"&lt;p&gt;&lt;b&gt;Caption&lt;/b&gt;: Malcolm Quine c. 2000. Photograph courtesy of the University of Sydney.&lt;/p&gt;&lt;p&gt;Malcolm Quine was born in Burton-on-Trent, Staffordshire, England on 10 July 1945. He went on to study at the University of London, London School of Economics, graduating with a Master of Science degree in 1967.&lt;/p&gt;&lt;p&gt;He won a Leverhulme Scholarship to study in Professor Pat Moran's Department of Statistics in the Institute of Advanced Studies at the Australian National University. He commenced his study there in 1968. Professor Moran suggested the topic of branching processes as a research area and asked Eugene Seneta, then a young Lecturer in the Department of Statistics, School of General Studies, the primarily teaching part of ANU, to look after Malcolm.&lt;/p&gt;&lt;p&gt;Malcolm's research went well, and a joint paper on branching processes, Quine and Seneta (&lt;span&gt;1969&lt;/span&gt;), was published in the &lt;i&gt;Australian Journal of Statistics&lt;/i&gt;. This work enabled Malcolm to enrol as a PhD student with Moran and Seneta as supervisors. Seneta was the principal supervisor guiding the research.&lt;/p&gt;&lt;p&gt;Malcolm was awarded his PhD in 1971 for his thesis entitled &lt;i&gt;Multitype Galton-Watson Processes&lt;/i&gt;. During his time at ANU, Malcolm rode a light motorbike round the campus as the two Statistics Departments were at opposite edges of the campus. At ANU Malcolm met his first wife Sue.&lt;/p&gt;&lt;p&gt;In 1972, he took up an appointment as a Lecturer in the Department of Mathematical Statistics at the University of Sydney. The Department Head at that time was Professor H.O. Lancaster. Malcolm stayed at the University of Sydney until his retirement in 2005, being promoted to Senior Lecturer in 1977 and Associate Professor in 1995.&lt;/p&gt;&lt;p&gt;He continued to publish high-quality research in the area of branching processes over a 30-year period, with several papers being joint with Wladek Szczotka, from the University of Wrocław.&lt;/p&gt;&lt;p&gt;At the University of Sydney Malcolm established a long collaboration with John Robinson. They published several papers on limit theorems for scores based on occupancy numbers, three of which appeared in &lt;i&gt;The Annals of Probability&lt;/i&gt;. They also had a major paper Quine and Robinson (&lt;span&gt;1985&lt;/span&gt;) on chi-square goodness-of-fit tests published in &lt;i&gt;The Annals of Statistics&lt;/i&gt;. Chi-square research was a well-established theme at the University of Sydney in the Lancaster years.&lt;/p&gt;&lt;p&gt;Eugene Seneta joined Malcolm at the University of Sydney as Professor and Head in mid-1979. They published a further two papers together in &lt;span&gt;1987&lt;/span&gt; and &lt;span&gt;1999&lt;/span&gt;. In 1993, following the demise of the Soviet Union, the two made a memorable and adventurous trip to the First World Congress on Branching Processes in Varna, Bulgaria. The paper Quine and Szczotka (&lt;span&gt;1995&lt;/span&gt;) was Malcolm's presentation.&lt;/p&gt;&lt;p&gt;Malcolm published three papers in &lt;i&gt;The Annals of Applied Probability&lt;/i&gt;. The first, Quine and Szczotka (&lt;span&gt;1994&lt;/span&gt;), was part of his body of w","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 4","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70067","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"John Llewelyn Hopper 20 May 1950–28 October 2024","authors":"John D. Mathews","doi":"10.1111/anzs.70065","DOIUrl":"https://doi.org/10.1111/anzs.70065","url":null,"abstract":"&lt;p&gt;&lt;b&gt;Caption:&lt;/b&gt; Professor John Hopper, AM. Photograph courtesy of Twin Research Australia.&lt;/p&gt;&lt;p&gt;The scientific world has mourned the loss of Professor John L. Hopper, AM, an outstanding biostatistician/epidemiologist who died after collapsing unexpectedly at a scientific meeting attended by Australian and international colleagues. He is remembered as a warm friend and colleague, honoured for his vision, his scientific achievements and his productivity. His leadership and seminal research transformed our understanding of how genes and environment interact to influence human health and disease, effectively establishing the discipline of genetic epidemiology in Australia. John Hopper left a great legacy not only through his work, but also through his passionate mentorship of generations of researchers and his unwavering commitment to generating rigorous evidence and following it wherever it led.&lt;/p&gt;&lt;p&gt;John grew up in a family that valued learning; his father, Victor Hopper, was professor of physics at the University of Melbourne and internationally known for his research on cosmic rays. John was similarly gifted. He was a top student at Box Hill High School in 1968 and later graduated with a BSc (Hons) and MSc from Monash University with prizes in maths and statistics. He first worked with the University of Melbourne from 1974 as a part-time tutor in mathematics and statistics before enrolling for his PhD with the Department of Mathematical Statistics at La Trobe University under the supervision of Professors Peter Brockwell and Niels Becker. In March 1980, John finished his PhD thesis entitled ‘Applications of Stochastic Models to Cell Kinetics and Epidemiology’ and looked for suitable employment.&lt;/p&gt;&lt;p&gt;As a young academic, John read widely in biostatistics and genetics and was greatly influenced by the work of RA Fisher and Sewall Wright. He was quick to realise that causal pathways could be better understood by using twin and family-based designs to estimate genetic and environmental effects. His enquiring mind also led him to take a deep interest in health and social issues, influencing his commitment to work in a health-related area of statistics.&lt;/p&gt;&lt;p&gt;It was my good fortune to meet John in 1980, to work closely with him for 5 years, and to become his long-time friend. In 1975, I had returned to Melbourne from my post-doctoral time in Oxford with Richard Doll and Richard Peto. With encouragement from Richard Lovell, and support from Nigel Gray at the Cancer Council, we had established a small epidemiological unit at the University of Melbourne and begun recruiting twins for research purposes in partnership with Nick Martin at ANU. By 1980, with NHMRC support, we were able to establish the Australian NHMRC Twin Registry, or Twin Research Australia, as it was subsequently known. That initial funding allowed us to employ John Hopper in full-time research. It was the start of his outstanding research career with the University of Melbourne. Ov","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 4","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70065","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Distance-Ordered Sign Scan and Run Tests for Symmetry: Exact Known-Median Calibration and Bootstrap Extensions","authors":"Ayman Baklizi","doi":"10.1111/anzs.70064","DOIUrl":"https://doi.org/10.1111/anzs.70064","url":null,"abstract":"<div>\u0000 \u0000 <p>We study distribution-free tests of univariate symmetry about a specified median <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {m}_0 $$</annotation>\u0000 </semantics></math>. The tests are constructed from the signs of observations after ordering the observations by their absolute distances from <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {m}_0 $$</annotation>\u0000 </semantics></math>. The first procedure is a two-sided scan test based on the maximum local imbalance of positive and negative signs over moving windows. The second procedure is a trimmed longest-run test, defined as the largest run of equal signs observed inside any window of fixed length. We give a precise Bernoulli/Rademacher notation for the ordered-sign construction, prove the exact distribution-free null property and describe finite Markov chain (FMCI) embedding algorithms for exact calibration. We add a local-alternative analysis that makes precise which departures from symmetry the scan statistic is designed to detect and how these differ from the targets of sign-, Wilcoxon-, runs- and longest-run tests. We also clarify the relation between the trimmed longest run and the ordinary longest run, discuss how the exact null distribution is affected when the median is estimated rather than specified, and describe a residual sign-flip calibration for applications to linear regression. A simulation study—including a model with asymmetry localised in distance from the median—compares the proposed tests with classical procedures, reports FMCI computation times and documents the complementary, rather than uniformly dominant, behaviour of the methods.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimating Functions Inference to Semi-Parametric Additive Models for Skewed And/Or Heavy-Tailed Longitudinal Data","authors":"João Victor B. de Freitas,&nbsp;Caio L. N. Azevedo,&nbsp;Juvêncio S. Nobre","doi":"10.1111/anzs.70063","DOIUrl":"https://doi.org/10.1111/anzs.70063","url":null,"abstract":"<p>In many fields of research, it is common to conduct experiments where several observations of the response variable are made on the same subject over non-random conditions, generating longitudinal studies. A wide variety of techniques deal with this type of data when analysing population variations, many based on estimating functions. It is also common to find longitudinal data where the assumption of asymmetry and/or heavy tails is necessary for the distribution associated with the outcome(s) and also where we do not know the relationship between these outcome(s) and the covariates. In these situations we can use the scale mixture of skew-normal distributions and the partially linear models. Said that, in this article, we developed estimating functions for the additive partially linear models based on the scale mixture of skew-normal distributions using a centred parameterisation. This parameterisation does not present inferential problems, as the non-quadratic form of the log-likelihood, that the classical skew-normal distribution can present. Additionally, it provides a better interpretation of the related parameters, since they represent the mean, variance and skewness coefficient. Our methodology focuses on the flexibility of the functional part when using semi-parametric models and also on the distributional flexibility and robustness when using the aforementioned class of distributions. Additionally, we presented residuals and influence diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of the estimators in finite samples. The methodology is illustrated with the analysis of the Framingham cholesterol study.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70063","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SigFPLS: A Signatures-Based Approach for Scalar-on-Function Regression Model","authors":"Jiakun Guo,&nbsp;Zhouping Li","doi":"10.1111/anzs.70061","DOIUrl":"https://doi.org/10.1111/anzs.70061","url":null,"abstract":"<div>\u0000 \u0000 <p>In functional data analysis, methods based on basis expansion are already well developed. However, when faced with collinearity in multivariate functional covariates, these methods may not perform effectively. In this paper, by using a new signature-based method, we introduce a novel method within the scalar-on-function regression framework, leveraging signature method and partial least squares (PLS), which we call <i>SigFPLS</i>. This method outperforms traditional functional regression models and the signature-based functional linear model by offering several key benefits: simple process for parameter tuning, easy implementation and effective handling of multicollinearity in multivariate functional data. Through extensive simulation studies and rigorous real data analysis, we demonstrate the effectiveness of our proposed method with focus on the scalar-on-function regression data, especially when dealing with multi-dimensional and rough functional covariates.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatial Scalar-on-Function Quantile Regression Model","authors":"Muge Mutis,&nbsp;Ufuk Beyaztas,&nbsp;Filiz Karaman,&nbsp;Han Lin Shang","doi":"10.1111/anzs.70062","DOIUrl":"https://doi.org/10.1111/anzs.70062","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper introduces a novel spatial scalar-on-function (SoF) quantile regression model that extends classical SoF models to account for spatial dependence and heterogeneous conditional distributions. The proposed model incorporates spatial autocorrelation through a spatially lagged response and characterises the entire conditional distribution of a scalar outcome given a functional predictor. To address endogeneity induced by the spatial lag term, we develop two robust estimation procedures based on instrumental variable (IV) strategies. The <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msqrt>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msqrt>\u0000 </mrow>\u0000 <annotation>$$ sqrt{n} $$</annotation>\u0000 </semantics></math>-consistency and asymptotic normality of the proposed estimators are established under mild regularity conditions. We demonstrate through extensive Monte Carlo simulations that the proposed estimators outperform existing mean-based and robust alternatives, particularly in settings with strong spatial dependence and outlier contamination. We apply our method to high-resolution environmental data from the Lombardy region in Italy, using daily ozone trajectories to predict daily mean concentrations of particulate matter with a diameter of less than 2.5 micrometers. The empirical results confirm the superiority of our approach in predictive accuracy, robustness and interpretability at various quantile levels. Our method has been implemented in the <span>ssofqrm</span> package.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148533259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coherent Forecasting of Ordinal Time Series With Application to Air-Quality Data","authors":"Christian H. Weiß,&nbsp;Osama Swidan,&nbsp;Layth C. Alwan","doi":"10.1111/anzs.70060","DOIUrl":"https://doi.org/10.1111/anzs.70060","url":null,"abstract":"<p>Motivated by an application to air quality data, we provide a comprehensive investigation of coherent forecasting techniques for ordinal time series. Here, the coherency requirement expresses that the computed forecast values have to be consistent with the ordered qualitative range of the data-generating process (DGP). Three classes of coherent forecasts are proposed, namely ordinal point forecasts, prediction intervals and probability mass function (pmf) forecasts. In addition, corresponding criteria for evaluating their predictive performance are established. An extensive simulation study analyses the performance of the coherent forecasting techniques across various ordinal DGPs, taking into account the impact of estimated model parameters and model misspecification. The proposed forecasting approaches are then applied to our central motivating application, the real-world time series on ordinal air quality levels and practical implications are discussed. In this context, it is also demonstrated that the coherent point and pmf forecasts can be combined visually in a meaningful and interpretable way. While centrally motivated by environmental monitoring, the proposed framework applies more broadly to ordinal time series arising in other settings where ordered categorical outcomes are used for assessment and decision making.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70060","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simultaneously Modelling Occurrence and Quantity of Multivariate Semicontinuous Data","authors":"Xingde Duan,&nbsp;Renjun Ma","doi":"10.1111/anzs.70059","DOIUrl":"https://doi.org/10.1111/anzs.70059","url":null,"abstract":"<p>Joint models have been developed recently for multivariate semicontinuous data; however, joint modelling implies structured covariance and nonnegative correlation among responses, and thus is inflexible in accommodating complex covariance structures in practice. In addition, zero-inflated continuous data have been traditionally handled by two-part mixed models where zero and positive responses are analysed separately; therefore, the multivariate nature of the data would be destroyed. In this paper, we introduce a new model for multivariate semicontinuous data by incorporating distribution-free multivariate random effects of unstructured covariance into Tweedie compound Poisson regression model. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of multivariate random effects. Our method is illustrated through the analysis of Mali family farmer data.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70059","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparing the Effectiveness of the Choropleth Map With a Hexagon Tile Map for Communicating Patterns in Australian Spatial Statistics","authors":"Stephanie Kobakian,&nbsp;Dianne Cook","doi":"10.1111/anzs.70058","DOIUrl":"https://doi.org/10.1111/anzs.70058","url":null,"abstract":"<p>The choropleth map is a common tool for communicating spatial distributions across geographic areas. However, the size of geographic units can distort interpretation, influencing how users perceive the distribution. A common alternative is the cartogram, which resizes areas based on population. Yet, in Australia, the stark disparities in geography and population make cartograms less suitable. We explore the hexagon tile map as an alternative. We report results from a task-based experiment involving human participants, using the lineup protocol to assess how well hexagon tile maps and choropleths convey spatial patterns. Three spatial patterns were tested: one reflecting geography, with values increasing monotonically from the northwest to southeast of Australia, and two with clustered high concentrations. Results show that the hexagon tile map outperforms the choropleth map. These findings support the use of alternative map displays and suggest that hexagon tile maps are effective for visualising spatial distributions in heterogeneous regions.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"68 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148174056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}