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Non-parametric depth-based tests for the multivariate location problem 多变量定位问题的非参数深度测试
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-06-29 DOI: 10.1111/anzs.12328
Sakineh Dehghan, Mohammad Reza Faridrohani
{"title":"Non-parametric depth-based tests for the multivariate location problem","authors":"Sakineh Dehghan,&nbsp;Mohammad Reza Faridrohani","doi":"10.1111/anzs.12328","DOIUrl":"10.1111/anzs.12328","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, using the notion of data depth, we describe two classes of affine invariant test statistics for the one-sample location problem. The tests are implemented through the idea of permutation tests. The performance of the test against some competitors is investigated with an extensive simulation study. It is observed that the tests perform well when compared to their competitors for a wide spectrum of alternatives. If the proposed test is defined based on a moment-free depth function, then it is not inherently required to have finite moments of any order and the tests have broader applicability than some of the existing tests. The robustness property of the proposed tests is considered with a simulation study. Finally, we apply the tests to a real data example.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12328","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80013153","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}
引用次数: 2
New moderation methods of higher school certificate assessments: a case study of the New South Wales practice 高等学校证书评估的新适度方法:新南威尔士州实践的案例研究
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-06-29 DOI: 10.1111/anzs.12317
Yanlin Shi
{"title":"New moderation methods of higher school certificate assessments: a case study of the New South Wales practice","authors":"Yanlin Shi","doi":"10.1111/anzs.12317","DOIUrl":"10.1111/anzs.12317","url":null,"abstract":"<div>\u0000 \u0000 <p>The Higher School Certificate (HSC) is the credential awarded to secondary school students in New South Wales (NSW), Australia. This paper reviews the current moderation process of the HSC and introduces and compares a range of modern statistical methods. With a comprehensive analysis of the complete 2013–2016 HSC results, we show that the monotone spline regression with the Huber loss function consistently beats the existing moderation method. With its simple structure, fast execution and improved effectiveness, this new moderation model is an ideal replacement of the in-force quadratic for the HSC practice in NSW.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12317","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87803813","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}
引用次数: 0
Forecasting the old-age dependency ratio to determine a sustainable pension age 预测老年抚养比，确定可持续的领取养老金年龄
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-06-29 DOI: 10.1111/anzs.12330
Rob J. Hyndman, Yijun Zeng, Han Lin Shang
{"title":"Forecasting the old-age dependency ratio to determine a sustainable pension age","authors":"Rob J. Hyndman,&nbsp;Yijun Zeng,&nbsp;Han Lin Shang","doi":"10.1111/anzs.12330","DOIUrl":"10.1111/anzs.12330","url":null,"abstract":"<div>\u0000 \u0000 <p>We forecast the old-age dependency ratio for Australia under various pension age proposals, and estimate a pension age scheme that will provide a stable old-age dependency ratio at a specified level. Our approach involves a stochastic population forecasting method based on coherent functional data models for mortality, fertility and net migration, which we use to simulate the future age-structure of the population. Our results suggest that the Australian pension age should be increased to 68 by 2030, 69 by 2036 and 70 by 2050, in order to maintain the old-age dependency ratio at 23%, just above the 2018 level. Our general approach can easily be extended to other target levels of the old-age dependency ratio and to other countries.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12330","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77019366","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}
引用次数: 6
A shared parameter mixture model for longitudinal income data with missing responses and zero rounding 具有缺失响应和零舍入的纵向收入数据共享参数混合模型
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-06-17 DOI: 10.1111/anzs.12323
Francis K.C. Hui, Howard D. Bondell
{"title":"A shared parameter mixture model for longitudinal income data with missing responses and zero rounding","authors":"Francis K.C. Hui,&nbsp;Howard D. Bondell","doi":"10.1111/anzs.12323","DOIUrl":"10.1111/anzs.12323","url":null,"abstract":"The analysis of longitudinal income data is often made challenging for several reasons. For example, in a national Australian survey on income over time, a non‐negligible proportion of responses are missing, and it is believed the missingness mechanism is non‐ignorable. Also, there are a large number of reported zero incomes, some of which may be true zeros (corresponding to individuals who legitimately do not earn an income), while some may be false zeros (corresponding to individuals choosing to round their income to zero). We propose a new shared parameter mixture (SPM) model for analysing semi‐continuous longitudinal income data, which addresses the two challenges of income non‐response and zero rounding. This is accomplished by jointly modelling an individual's underlying income together with the probability of missingness and rounding to zero, where both probabilities are permitted to vary in a smooth manner with their underlying non‐zero income. Applying the SPM model to the Australian income survey reveals that on average, older female individuals and individuals with a long‐term health condition are considerably less likely to earn an income, while income tended to be highest for male individuals on fixed‐term/permanent job contracts between ages 50 and 60. Furthermore there is evidence of both zero rounding, and conditional on the assumed missingness mechanism, individuals with incomes at the higher and lower ends are more likely to not report their income.","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12323","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89592499","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}
引用次数: 0
Adversarial risk analysis for first-price sealed-bid auctions 首价密封拍卖的对抗风险分析
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-06-01 DOI: 10.1111/anzs.12315
Muhammad Ejaz, Chaitanya Joshi, Stephen Joe
{"title":"Adversarial risk analysis for first-price sealed-bid auctions","authors":"Muhammad Ejaz,&nbsp;Chaitanya Joshi,&nbsp;Stephen Joe","doi":"10.1111/anzs.12315","DOIUrl":"10.1111/anzs.12315","url":null,"abstract":"<div>\u0000 \u0000 <p>Adversarial risk analysis (ARA) is an upcoming methodology that is considered to have advantages over the traditional decision-theoretic and game-theoretic approaches. ARA solutions for first-price sealed-bid (FPSB) auctions have been found but only under strong assumptions which make the model somewhat unrealistic. In this paper, we use ARA methodology to model FPSB auctions using more realistic assumptions. We define a new utility function that considers bidders’ wealth, we assume a reserve price and find solutions not only for risk-neutral but also for risk-averse as well as risk-seeking bidders. We model the problem using ARA for non-strategic play and level-<i>k</i> thinking solution concepts.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12315","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75026347","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}
引用次数: 5
On distance based goodness of fit tests for missing data when missing occurs at random 缺失数据随机发生时基于距离的拟合优度检验
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-30 DOI: 10.1111/anzs.12313
Subhra Sankar Dhar, Ujjwal Das
{"title":"On distance based goodness of fit tests for missing data when missing occurs at random","authors":"Subhra Sankar Dhar,&nbsp;Ujjwal Das","doi":"10.1111/anzs.12313","DOIUrl":"10.1111/anzs.12313","url":null,"abstract":"<div>\u0000 \u0000 <p>Various non-parametric goodness of fit tests have already been investigated in the literature. However, those tests are rarely used in the case of missing observations. We here study the goodness of fit test for missing data based on <i>L</i><sub><i>p</i></sub> distances along with Kolmogorov–Smirnov and Cramer–von-Mises distances when missingness occurs at random. The asymptotic distributions of the proposed test statistics have been derived under contiguous alternatives that enable us to investigate the asymptotic local power of the tests. We also study the performance of the tests for finite samples using simulation, and the tests perform well for those cases. The usefulness of the tests is illustrated on three real data sets.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12313","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81486366","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}
引用次数: 0
Bayesian decision rules to classification problems 分类问题的贝叶斯决策规则
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-24 DOI: 10.1111/anzs.12325
Yuqi Long, Xingzhong Xu
{"title":"Bayesian decision rules to classification problems","authors":"Yuqi Long,&nbsp;Xingzhong Xu","doi":"10.1111/anzs.12325","DOIUrl":"10.1111/anzs.12325","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we analysed classification rules under Bayesian decision theory. The setup we considered here is fairly general, which can represent all possible parametric models. The Bayes classification rule we investigated minimises the Bayes risk under general loss functions. Among the existing literatures, the 0-1 loss function appears most frequently, under which the Bayes classification rule is determined by the posterior predictive densities. Theoretically, we extended the Bernstein–von Mises theorem to the multiple-sample case. On this basis, the oracle property of Bayes classification rule has been discussed in detail, which refers to the convergence of the Bayes classification rule to the one built from the true distributions, as the sample size tends to infinity. Simulations show that the Bayes classification rules do have some advantages over the traditional classifiers, especially when the number of features approaches the sample size.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12325","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89269715","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}
引用次数: 1
Globally intensity-reweighted estimators for K- and pair correlation functions K-和对相关函数的全局强度重加权估计
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-17 DOI: 10.1111/anzs.12318
Thomas Shaw, Jesper M⊘ller, Rasmus Plenge Waagepetersen
{"title":"Globally intensity-reweighted estimators for K- and pair correlation functions","authors":"Thomas Shaw,&nbsp;Jesper M⊘ller,&nbsp;Rasmus Plenge Waagepetersen","doi":"10.1111/anzs.12318","DOIUrl":"10.1111/anzs.12318","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce new estimators of the inhomogeneous <i>K</i>-function and the pair correlation function of a spatial point process as well as the cross <i>K</i>-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12318","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75341203","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}
引用次数: 9
A few statistical principles for data science 数据科学的一些统计原则
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-08 DOI: 10.1111/anzs.12324
Noel Cressie
{"title":"A few statistical principles for data science","authors":"Noel Cressie","doi":"10.1111/anzs.12324","DOIUrl":"10.1111/anzs.12324","url":null,"abstract":"<div>\u0000 \u0000 <p>In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas are continually being annexed into Data Science. For example, biometrics was traditionally statistics for agriculture in all its forms but now, in Data Science, it means the study of characteristics that can be used to identify an individual. Examples of non-intrusive measurements include height, weight, fingerprints, retina scan, voice, photograph/video (facial landmarks and facial expressions) and gait. A multivariate analysis of such data would be a complex project for a statistician, but a software engineer might appear to have no trouble with it at all. In any applied-statistics project, the statistician worries about uncertainty and quantifies it by modelling data as realisations generated from a probability space. Another approach to uncertainty quantification is to find similar data sets, and then use the variability of results between these data sets to capture the uncertainty. Both approaches allow ‘error bars’ to be put on estimates obtained from the original data set, although the interpretations are different. A third approach, that concentrates on giving a single answer and gives up on uncertainty quantification, could be considered as Data Engineering, although it has staked a claim in the Data Science terrain. This article presents a few (actually nine) statistical principles for data scientists that have helped me, and continue to help me, when I work on complex interdisciplinary projects.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12324","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82540496","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}
引用次数: 4
Information criteria for inhomogeneous spatial point processes 非齐次空间点过程的信息准则
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-08 DOI: 10.1111/anzs.12327
Achmad Choiruddin, Jean-François Coeurjolly, Rasmus Waagepetersen
{"title":"Information criteria for inhomogeneous spatial point processes","authors":"Achmad Choiruddin,&nbsp;Jean-François Coeurjolly,&nbsp;Rasmus Waagepetersen","doi":"10.1111/anzs.12327","DOIUrl":"10.1111/anzs.12327","url":null,"abstract":"<div>\u0000 \u0000 <p>The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain and combinations of these. For inhomogeneous Poisson processes we consider Akaike's information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of ‘sample size’ needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12327","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80429406","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}
引用次数: 24
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