Australian & New Zealand Journal of Statistics最新文献

{"title":"Bayesian hypothesis tests with diffuse priors: Can we have our cake and eat it too?","authors":"J. T. Ormerod,&nbsp;M. Stewart,&nbsp;W. Yu,&nbsp;S. E. Romanes","doi":"10.1111/anzs.12410","DOIUrl":"10.1111/anzs.12410","url":null,"abstract":"<p>We propose a new class of priors for Bayesian hypothesis testing, which we name ‘cake priors’. These priors circumvent the Jeffreys–Lindley paradox (also called Bartlett's paradox) a problem associated with the use of diffuse priors leading to nonsensical statistical inferences. Cake priors allow the use of diffuse priors (having one's cake) while achieving theoretically justified inferences (eating it too). We demonstrate this methodology for Bayesian hypotheses tests for various common scenarios. The resulting Bayesian test statistic takes the form of a penalised likelihood ratio test statistic. Under typical regularity conditions, we show that Bayesian hypothesis tests based on cake priors are Chernoff consistent, that is, achieve zero type I and II error probabilities asymptotically. We also discuss Lindley's paradox and argue that the paradox occurs with small and vanishing probability as sample size increases.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"66 2","pages":"204-227"},"PeriodicalIF":1.1,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.12410","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140182403","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":"Asymptotics for the conditional self-weighted \u0000 \u0000 \u0000 M\u0000 \u0000 $$ M $$\u0000 estimator of GRCA(\u0000 \u0000 \u0000 p\u0000 \u0000 $$ p $$\u0000 ) models and its statistical inference","authors":"Chi Yao,&nbsp;Wei Yu,&nbsp;Xuejun Wang","doi":"10.1111/anzs.12408","DOIUrl":"10.1111/anzs.12408","url":null,"abstract":"<div>\u0000 \u0000 <p>Under the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ p $$</annotation>\u0000 </semantics></math>-order generalised random coefficient autoregressive (GRCA(<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ p $$</annotation>\u0000 </semantics></math>)) model with random coefficients <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>Φ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>,</mo>\u0000 </mrow>\u0000 <annotation>$$ {boldsymbol{Phi}}_t, $$</annotation>\u0000 </semantics></math> we propose a conditional self-weighted <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 </mrow>\u0000 <annotation>$$ M $$</annotation>\u0000 </semantics></math> estimator of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <msub>\u0000 <mrow>\u0000 <mi>Φ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ mathrm{E}{boldsymbol{Phi}}_t $$</annotation>\u0000 </semantics></math>. We investigate the asymptotic normality of this estimator with possibly heavy-tailed random variables. Furthermore, a Wald test statistic is constructed for the linear restriction on the parameters. In addition, the simulation experiments are carried out to assess the finite sample performance of theoretical results. Finally, a real data analysis about the increase (%) in the number of construction projects this year over the same period of last year is provided.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"66 1","pages":"103-124"},"PeriodicalIF":1.1,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139954304","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":"Unified robust estimation","authors":"Zhu Wang","doi":"10.1111/anzs.12409","DOIUrl":"10.1111/anzs.12409","url":null,"abstract":"<div>\u0000 \u0000 <p>Robust estimation is primarily concerned with providing reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. In modern penalised generalised linear models (GLMs), however, there is limited research on robust estimation that can provide weights to determine the outlier status of the observations. This article proposes a unified framework based on a large family of loss functions, a composite of concave and convex functions (CC-family). Properties of the CC-family are investigated, and CC-estimation is innovatively conducted via the iteratively reweighted convex optimisation (IRCO), which is a generalisation of the iteratively reweighted least squares in robust linear regression. For robust GLM, the IRCO becomes the iteratively reweighted GLM. The unified framework contains penalised estimation and robust support vector machine (SVM) and is demonstrated with a variety of data applications.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"66 1","pages":"77-102"},"PeriodicalIF":1.1,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953816","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":"Latent heterogeneity in COVID-19 hospitalisations: a cluster-weighted approach to analyse mortality","authors":"Paolo Berta,&nbsp;Salvatore Ingrassia,&nbsp;Giorgio Vittadini,&nbsp;Daniele Spinelli","doi":"10.1111/anzs.12407","DOIUrl":"10.1111/anzs.12407","url":null,"abstract":"<p>The COVID-19 pandemic caused an unprecedented excess mortality. Since 2020, many studies have focussed on the characteristics of COVID-19 patients who did not survive. From the statistical point of view, what seems to dominate is the large heterogeneity of the populations affected by COVID-19 and the extreme difficulty in identifying subpopulations who died affected by a plurality of contemporary characteristics. In this paper, we propose an extremely flexible approach based on a cluster-weighted model, which allows us to identify latent groups of patients sharing similar characteristics at the moment of hospitalisation as well as a similar mortality. We focus on one of the hardest hit areas in Italy and study the heterogeneity in the population of patients affected by COVID-19 using administrative data on hospitalisations in the first wave of the pandemic. Results highlighted that a model-based clustering approach is essential to understand the complexity of the COVID-19 patients treated by hospitals and who die during hospitalisation.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"66 1","pages":"1-20"},"PeriodicalIF":1.1,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.12407","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772597","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":"A novel response model and target selection method with applications to marketing","authors":"Y. Cai","doi":"10.1111/anzs.12406","DOIUrl":"10.1111/anzs.12406","url":null,"abstract":"<p>Response models used in marketing are not always constructed for later marketing optimisation, which often results in unsatisfactory results in target selection for future marketing activities. To solve this problem, we develop a new binary response model and a new marketing target selection method. The proposed model can predict multiple propensity scores per customer through customer-specific propensity score distributions, which is not possible with existing response models, filling a gap in the literature. The target selection method can determine the best propensity scores from those predicted by the proposed model and use them to select customers for further marketing activities. Our simulation results and application to real marketing data confirm that the performance of the proposed model in target selection is significantly better than that of the existing models, including some popular machine learning methods, which indicate that our method can be very useful in practice.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"66 1","pages":"48-76"},"PeriodicalIF":1.1,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.12406","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515508","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":"Identifying changes in the distribution of income from higher-order moments with an application to Australia","authors":"Vance L. Martin,&nbsp;Jialu Shi,&nbsp;Yang Song,&nbsp;Wenying Yao","doi":"10.1111/anzs.12405","DOIUrl":"10.1111/anzs.12405","url":null,"abstract":"<p>Changes in the distribution of income over time are identified based on an adjusted two-sample version of the Neyman smooth test by using subsampling methods to approximate the sampling distribution of the test statistic when samples are not independent of each other. A range of Monte Carlo experiments show that the approach corrects for size distortions arising from dependent samples as well as generating monotonic power functions. Applying the approach to studying the distribution of income in Australia over the business cycle and the Global Financial Crisis, the empirical results highlight the importance of higher-order moments and demonstrate that business cycles are not all alike as the relative strengths of higher-order moments vary over phases of the cycle.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"66 1","pages":"21-47"},"PeriodicalIF":1.1,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.12405","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515413","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":"Exact testing for heteroscedasticity in a two-way layout in variety frost trials when incorporating a covariate","authors":"Angelika A. Pilkington,&nbsp;Brenton R. Clarke,&nbsp;Dean A. Diepeveen","doi":"10.1111/anzs.12404","DOIUrl":"10.1111/anzs.12404","url":null,"abstract":"<p>Two-way layouts are common in grain industry research where it is often the case that there are one or more covariates. It is widely recognised that when estimating fixed effect parameters, one should also examine for possible extra error variance structure. An exact test for heteroscedasticity, when there is a covariate, is illustrated for a data set from frost trials in Western Australia. While the general algebra for the test is known, albeit in past literature, there are computational aspects of implementing the test for the two way when there are covariates. In this scenario the test is shown to have greater power than the industry standard, and because of its exact size, is preferable to use of the restricted maximum likelihood ratio test (REMLRT) based on the approximate asymptotic distribution in this instance. Formulation of the exact test considered here involves creation of appropriate contrasts in the experimental design. This is illustrated using specific choices of observations corresponding to an index set in the linear model for the two-way layout. Also an algorithm supplied complements the test. Comparisons of size and power then ensue. The test has natural extensions when there are unbalanced data, and more than one covariate may be present. Results can be extended to Balanced Incomplete Block Designs.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"65 4","pages":"309-326"},"PeriodicalIF":0.8,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.12404","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078183","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":"Exact likelihoods for N-mixture models with time-to-detection data","authors":"Linda M. Haines,&nbsp;Res Altwegg,&nbsp;D. L. Borchers","doi":"10.1111/anzs.12401","DOIUrl":"10.1111/anzs.12401","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is concerned with the formulation of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$$ N $$</annotation>\u0000 </semantics></math>-mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses time-to-first-detection within the context of detection/non-detection and time-to-each-detection and time-to-first-detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed-form expressions for the likelihoods associated with time-to-detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times-to-detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times-to-detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times-to-detection in addition to the count data. An <span>R</span> package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"65 4","pages":"327-343"},"PeriodicalIF":0.8,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567024","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":"Model averaged tail area confidence intervals in nested linear regression models","authors":"Paul Kabaila,&nbsp;Ayesha Perera","doi":"10.1111/anzs.12402","DOIUrl":"10.1111/anzs.12402","url":null,"abstract":"<div>\u0000 \u0000 <p>The performance, in terms of coverage and expected length, of the model averaged tail area (MATA) confidence interval, proposed by Turek &amp; Fletcher (2012, <i>Computational Statistics &amp; Data Analysis</i>, 56, 2809–2815), depends greatly on the data-based model weights used in its construction. We generalise the computationally convenient exact formulae due to Kabaila, Welsh &amp; Abeysekera (2016, <i>Scandinavian Journal of Statistics</i>, 43, 35–48) for the coverage and expected length of this confidence interval for two nested linear regression models to the case of two or more nested linear regression models. This permits the numerical assessment of the performance, in terms of coverage probability and scaled expected length, of the MATA confidence interval for any given data-based model weights in the context of three or more nested linear regression models. We illustrate this numerical assessment of performance of the MATA confidence interval, for model weights based on any given Generalised Information Criterion, in the context of three nested linear regression models using the real life ‘Cholesterol’ data. This provides a very informative further exploration of the influence of these model weights on the performance of this confidence interval.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"65 4","pages":"364-378"},"PeriodicalIF":0.8,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138548308","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 role of pairwise matching in experimental design for an incidence outcome","authors":"Adam Kapelner,&nbsp;Abba M. Krieger,&nbsp;David Azriel","doi":"10.1111/anzs.12403","DOIUrl":"10.1111/anzs.12403","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider the problem of evaluating designs for a two-arm randomised experiment with an incidence (binary) outcome under a non-parametric general response model. Our two main results are that the a priori pair matching design is (1) the optimal design as measured by mean squared error among all block designs which includes complete randomisation. And (2), this pair-matching design is minimax, that is, it provides the lowest mean squared error under an adversarial response model. Theoretical results are supported by simulations and clinical trial data where we demonstrate the superior performance of pairwise matching designs under realistic conditions.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"65 4","pages":"379-393"},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138517672","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}