Australian & New Zealand Journal of Statistics最新文献

{"title":"Homogeneity and Sparsity Pursuit Using Robust Adaptive Fused Lasso","authors":"Le Chang,&nbsp;Yanlin Shi","doi":"10.1111/anzs.70010","DOIUrl":"https://doi.org/10.1111/anzs.70010","url":null,"abstract":"<p>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.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"157-174"},"PeriodicalIF":0.8,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615493","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":"High-dimensional graphical inference via partially penalised regression","authors":"Ni Zhao,&nbsp;Zemin Zheng,&nbsp;Yang Li","doi":"10.1111/anzs.70005","DOIUrl":"https://doi.org/10.1111/anzs.70005","url":null,"abstract":"<div>\u0000 \u0000 <p>Graphical models are important tools to characterise the conditional independence structure among a set of variables. Despite the rapid development of statistical inference for high-dimensional graphical models, existing methods typically need a stringent constraint on the sample size. In this paper, we develop a new graphical projection estimator (GPE) for statistical inference in Gaussian graphical models via partially penalised regression. The suggested inference procedure takes advantage of the strong signals, which can be identified in advance, and utilises partially penalised regression to avoid the penalisation on them when constructing the GPE. It leads to enhanced inference efficiency by removing the impacts of strong signals that contribute to the bias term. We show that the proposed GPE can enjoy asymptotic normality under a relaxed constraint on the sample size, which is of the same order as that needed for consistent estimation. The usefulness of our method is demonstrated through simulations and a prostate tumour gene expression dataset.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"265-291"},"PeriodicalIF":0.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615012","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":"How data or error covariance can change and still retain BLUEs as well as their covariance or the sum of squares of errors","authors":"Stephen J. Haslett,&nbsp;Jarkko Isotalo,&nbsp;Augustyn Markiewicz,&nbsp;Simo Puntanen","doi":"10.1111/anzs.70003","DOIUrl":"https://doi.org/10.1111/anzs.70003","url":null,"abstract":"<p>Misspecification of the error covariance in linear models usually leads to incorrect inference and conclusions. We consider two linear models, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$$ mathcal{A} $$</annotation>\u0000 </semantics></math>\u0000and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <annotation>$$ mathcal{B} $$</annotation>\u0000 </semantics></math>, with the same design matrix but different error covariance matrices. The conditions under which every representation of the best linear unbiased estimator (BLUE) of any estimable parametric vector under <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$$ mathcal{A} $$</annotation>\u0000 </semantics></math> remains BLUE under <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <annotation>$$ mathcal{B} $$</annotation>\u0000 </semantics></math>\u0000have been well known since C.R. Rao's paper in 1971: Unified theory of linear estimation, <i>Sankhyā Ser. A</i>, Vol. 33, pp. 371–394. However, there are no previously published results on retaining the weighted sum of squares of errors (SSE) for non-full-rank design or error covariance matrices, and the question of when the covariance matrix of the BLUEs is also retained has been partially explored only recently. For change in any specified error covariance matrix, we provide necessary and sufficient conditions (nasc) for both BLUEs and their covariance matrix to remain unaltered and to retain this property for all submodels. We also consider nasc for SSE to be unchanged. We decompose SSE under error covariance changes, and derive nasc under which error covariance change leaves hypothesis tests for fixed-effect deletion under normality unaltered. We also show that simultaneous retention of BLUEs and both their covariance and SSE is not possible. We outline the effects of weak and strong error covariance singularity. We provide applications (via data cloning) to maintaining data confidentiality in Official Statistics without using Confidentialised Unit Record Files (CURFs), to certain types of experimental design and to estimation of fixed parameters for linear models for single nucleotide polymorphisms (SNPs) in genetics.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"175-201"},"PeriodicalIF":0.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615521","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":"Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science. By Aubrey Clayton, New York, Columbia University Press, 1st ed., 2021. 368 pages. AU$ 57.95 (hardcover). ISBN: 10:0231199945.","authors":"Mahdi Nouraie","doi":"10.1111/anzs.70007","DOIUrl":"https://doi.org/10.1111/anzs.70007","url":null,"abstract":"","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"344-345"},"PeriodicalIF":0.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615516","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":"Autocovariance function estimation via difference schemes for a semiparametric change point model with \u0000 \u0000 \u0000 m\u0000 \u0000 $$ m $$\u0000 -dependent errors","authors":"Michael Levine,&nbsp;Inder Tecuapetla-Gómez","doi":"10.1111/anzs.70002","DOIUrl":"https://doi.org/10.1111/anzs.70002","url":null,"abstract":"<div>\u0000 \u0000 <p>We discuss a broad class of difference-based estimators of the autocovariance function in a semiparametric regression model where the signal consists of the sum of a smooth function and another stepwise function whose number of jumps and locations are unknown (change points) while the errors are stationary and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$$ m $$</annotation>\u0000 </semantics></math>-dependent. We establish that the influence of the smooth part of the signal over the bias of our estimators is negligible; this is a general result as it does not depend on the distribution of the errors. We show that the influence of the unknown smooth function is negligible also in the mean squared error (MSE) of our estimators. Although we assumed Gaussian errors to derive the latter result, our finite sample studies suggest that the class of proposed estimators still show small MSE when the errors are not Gaussian. Our simulation study also demonstrates that, when the error process is mis-specified as an AR<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ (1) $$</annotation>\u0000 </semantics></math> instead of an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$$ m $$</annotation>\u0000 </semantics></math>-dependent process, our proposed method can estimate autocovariances about as well as some methods specifically designed for the AR(1) case, and sometimes even better than them. We also allow both the number of change points and the magnitude of the largest jump grow with the sample size <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$$ n $$</annotation>\u0000 </semantics></math>. In this case, we provide conditions on the interplay between the growth rate of these two quantities as well as the vanishing rate of the modulus of continuity (of the signal's smooth part) that ensure <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 of our autocovariance estimators. As an application, we use our approach to provide a better understanding of the possible autocovariance structure of a time series of global averaged annual temperature anomalies. Finally, the <span>R</span> package <span>dbacf</span> complements this article.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"202-223"},"PeriodicalIF":0.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615522","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":"Functional Data Analysis with R. By C. M. Crainiceanu, J. Goldsmith, A. Leroux, and E. Cui, Boca Raton, FL: Chapman and Hall/CRC. 2024. 338 pages. AU$ 138.40 (hardback). ISBN: 978-1-032-24471-6.","authors":"Faïcel Chamroukhi","doi":"10.1111/anzs.70006","DOIUrl":"https://doi.org/10.1111/anzs.70006","url":null,"abstract":"","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"341-343"},"PeriodicalIF":0.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615518","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":"Statistical balancing as an unconstrained optimisation problem","authors":"N. T. Longford","doi":"10.1111/anzs.70004","DOIUrl":"https://doi.org/10.1111/anzs.70004","url":null,"abstract":"<div>\u0000 \u0000 <p>Within the potential outcomes framework, balancing the treatment groups is a key step in estimating the average treatment effect in an observational study. Methods for optimal matching or weighting solve nonlinear programming problems. We present an alternative, related to ridge regression. Its solution has a closed form and is a smooth function of a set of tuning parameters. The method is accompanied by a simple way of exploring the sensitivity with respect to bias due to an unobserved confounder. It is applied to retrospective studies in neonatal research, concerned with clinical care for preterm born babies in the first few weeks of their lives.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"292-319"},"PeriodicalIF":0.8,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615515","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":"The incremental progression from fixed to random factors in the analysis of variance: a new synthesis","authors":"Marti J. Anderson,&nbsp;Ray N. Gorley,&nbsp;Antonio Terlizzi","doi":"10.1111/anzs.70001","DOIUrl":"https://doi.org/10.1111/anzs.70001","url":null,"abstract":"<p>Classically, the distinction between a fixed versus a random factor in analysis of variance has been considered a binary choice. Here we consider that any given factor can also occur along an incremental series of steps between these two extremes, depending on the sampling fraction of its levels from the wider population. Fixed factors occur where all possible levels are drawn, and random factors occur in the limit as the population of possible levels approaches infinity. When some identifiable fraction of a finite population of possible levels is drawn, the factor can be thought of as something in between fixed and random, and can be analysed explicitly as finite directly within the analysis of variance (ANOVA) framework. Requiring explicit specification of the population size from which observed levels are drawn for each factor, we provide a unified approach to derive expectations of mean squares (EMS) in ANOVA for any types of factors along the entire graded progression from fixed to random, inclusive, that may be nested within or crossed with one another, from balanced, asymmetrical or unbalanced designs, including multi-level hierarchical sampling designs, mixed models and interactions. Implications for estimation of variance components, tailored bootstrap methods and tests of hypotheses under minimal assumptions of exchangeability are described and further extended to multivariate dissimilarity-based settings.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 1","pages":"3-30"},"PeriodicalIF":0.8,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143831039","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":"Least-squares estimators of the linear-by-linear association parameter from an ordinal log-linear model","authors":"Eric J. Beh,&nbsp;Sidra Zafar,&nbsp;Irene L. Hudson","doi":"10.1111/anzs.70000","DOIUrl":"https://doi.org/10.1111/anzs.70000","url":null,"abstract":"<p>When modelling the association between the ordinal categorical variables of a contingency table, ordinal log-linear models are typically used; these models are a variation of the more popular log-linear model, which has attracted considerable attention in the statistics and allied literature since the late 1960s. Estimating the parameters of an ordinal log-linear model usually involves the use of iterative techniques, typically Newton's method and iterative proportional fitting. However, the early 2000s brought with it more direct estimation methods that do not require the use of iterative techniques. When the focus is on the parameter that reflects the linear-by-linear association between the variables, these methods have proven to provide unbiased, consistent and normally distributed estimates. Despite this new work, no attention has been given to the estimation of the least-squares estimator. Therefore, this article derives the least-squares estimator of the linear-by-linear association parameter and shows it to be equivalent to one of the existing non-iterative estimators recently described. We also derive two further least-squares estimators based on the Box-Cox transformation and derive their variance.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"137-156"},"PeriodicalIF":0.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615167","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":"spbal: An R package for spatially balanced master sampling","authors":"B. L. Robertson,&nbsp;P. Davies,&nbsp;O. Gansell,&nbsp;P. van Dam-Bates,&nbsp;T. McDonald","doi":"10.1111/anzs.12435","DOIUrl":"https://doi.org/10.1111/anzs.12435","url":null,"abstract":"<p>One of the most critical design features for sampling spatial populations is being able to draw spatially balanced samples. A substantial body of literature on sampling methodology has shown that spatially balanced samples can improve the precision of commonly used design-based estimators in various settings. Spatially balanced master samples offer several practical advantages for practitioners, including adjusting the sample size to match budgetary constraints, intensifying a previous sample or defining a panel design for surveying over time. These designs are of practical importance and should be easy to generate with reliable and efficient software. The <span>spbal</span> <span>R</span> package provides explicit functionality for spatially balanced master sampling designs from point and areal resources. Stratified and panel designs are also possible with <span>spbal</span>. In this article, we demonstrate the flexibility of <span>spbal</span> with several example designs using spatial populations from New Zealand.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 2","pages":"320-336"},"PeriodicalIF":0.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.12435","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615078","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}