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Australian & New Zealand Journal of Statistics最新文献

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Depth and outliers for samples of sets and random sets distributions 集和随机集分布样本的深度和离群值
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-07 DOI: 10.1111/anzs.12326
Ignacio Cascos, Qiyu Li, Ilya Molchanov
{"title":"Depth and outliers for samples of sets and random sets distributions","authors":"Ignacio Cascos,&nbsp;Qiyu Li,&nbsp;Ilya Molchanov","doi":"10.1111/anzs.12326","DOIUrl":"10.1111/anzs.12326","url":null,"abstract":"<div>\u0000 \u0000 <p>We suggest several constructions suitable to define the depth of set-valued observations with respect to a sample of convex sets or with respect to the distribution of a random closed convex set. With the concept of a depth, it is possible to determine if a given convex set should be regarded an outlier with respect to a sample of convex closed sets. Some of our constructions are motivated by the known concepts of half-space depth and band depth for function-valued data. A novel construction derives the depth from a family of non-linear expectations of random sets. Furthermore, we address the role of positions of sets for evaluation of their depth. Two case studies concern interval regression for Greek wine data and detection of outliers in a sample of particles.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12326","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88387347","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
Infill asymptotics for adaptive kernel estimators of spatial intensity 空间强度自适应核估计的填充渐近性
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-07 DOI: 10.1111/anzs.12319
M.N.M. van Lieshout
{"title":"Infill asymptotics for adaptive kernel estimators of spatial intensity","authors":"M.N.M. van Lieshout","doi":"10.1111/anzs.12319","DOIUrl":"10.1111/anzs.12319","url":null,"abstract":"We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12319","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80890931","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}
引用次数: 3
Modelling columnarity of pyramidal cells in the human cerebral cortex 模拟人类大脑皮层锥体细胞的柱状结构
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-06 DOI: 10.1111/anzs.12321
Andreas Dyreborg Christoffersen, Jesper M⊘ller, Heidi S⊘gaard Christensen
{"title":"Modelling columnarity of pyramidal cells in the human cerebral cortex","authors":"Andreas Dyreborg Christoffersen,&nbsp;Jesper M⊘ller,&nbsp;Heidi S⊘gaard Christensen","doi":"10.1111/anzs.12321","DOIUrl":"10.1111/anzs.12321","url":null,"abstract":"<div>\u0000 \u0000 <p>For modelling the location of pyramidal cells in the human cerebral cortex, we suggest a hierarchical point process in that exhibits anisotropy in the form of cylinders extending along the <i>z</i>-axis. The model consists first of a generalised shot noise Cox process for the <i>xy</i>-coordinates, providing cylindrical clusters, and next of a Markov random field model for the <i>z</i>-coordinates conditioned on the <i>xy</i>-coordinates, providing either repulsion, aggregation or both within specified areas of interaction. Several cases of these hierarchical point processes are fitted to two pyramidal cell data sets, and of these a final model allowing for both repulsion and attraction between the points seem adequate. We discuss how the final model relates to the so-called minicolumn hypothesis in neuroscience.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86876749","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: 7
Model-based inference using judgement post-stratified samples in finite populations 基于模型的推理，在有限种群中使用判断后分层样本
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-05-06 DOI: 10.1111/anzs.12320
Omer Ozturk, Konul Bayramoglu Kavlak
{"title":"Model-based inference using judgement post-stratified samples in finite populations","authors":"Omer Ozturk,&nbsp;Konul Bayramoglu Kavlak","doi":"10.1111/anzs.12320","DOIUrl":"10.1111/anzs.12320","url":null,"abstract":"<div>\u0000 \u0000 <p>In survey sampling studies, statistical inference can be constructed either using design based randomisation or super population model. Design-based inference using judgement post-stratified (JPS) sampling is available in the literature. This paper develops statistical inference based on super population model in a finite population setting using JPS sampling design. For a JPS sample, first a simple random sample (SRS) is constructed without replacement. The sample units in this SRS are then stratified based on judgement ranking in a small comparison set to induce a data structure in the sample. The paper shows that the mean of a JPS sample is model unbiased and has smaller mean square prediction error (MSPE) than the MSPE of a simple random sample mean. Using an unbiased estimator of the MSPE, the paper also constructs prediction confidence interval for the population mean. A small-scale empirical study shows that the JPS sample predictor performs better than an SRS predictor when the quality of ranking information in JPS sampling is not poor. The paper also shows that the coverage probabilities of prediction intervals are very close to the nominal coverage probability. Proposed inferential procedure is applied to a real data set obtained from an agricultural research farm.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12320","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89597791","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
Stereological inference on mean particle shape from vertical sections 垂直剖面平均粒子形状的立体推理
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-03-09 DOI: 10.1111/anzs.12309
Eva B. Vedel Jensen
{"title":"Stereological inference on mean particle shape from vertical sections","authors":"Eva B. Vedel Jensen","doi":"10.1111/anzs.12309","DOIUrl":"10.1111/anzs.12309","url":null,"abstract":"<div>\u0000 \u0000 <p>It was a major breakthrough when design-based stereological methods for <i>vertical sections</i> were developed by Adrian Baddeley and coworkers in the 1980s. Most importantly, it was shown how to estimate in a design-based fashion surface area from observations in random vertical sections with uniform position and uniform rotation around the vertical axis. The great practical importance of these developments is due to the fact that some biostructures can only be recognised on vertical sections. Later, local design-based estimation of mean particle volume from vertical sections was developed. In the present paper, we review these important advances in stereology. Quite recently, vertical sections have gained renewed interest, since it has been shown that mean particle shape can be estimated from such sections. These new developments are also reviewed in the present paper.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12309","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73552048","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
Projection properties of three-level screening designs 三级筛分设计的投影特性
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-02-22 DOI: 10.1111/anzs.12306
Mohammed A. Alomair, Stelios D. Georgiou, Manohar Aggarwal
{"title":"Projection properties of three-level screening designs","authors":"Mohammed A. Alomair,&nbsp;Stelios D. Georgiou,&nbsp;Manohar Aggarwal","doi":"10.1111/anzs.12306","DOIUrl":"10.1111/anzs.12306","url":null,"abstract":"<div>\u0000 \u0000 <p>Screening designs are important for finding the factors that have a major effect on industrial experiments. In regard to quantitative factors, certain experimenters prefer three-level rather than two-level factors because having three levels can provide some assessments for capturing curvature in the response. In a recent paper, Jones and Nachtsheim, <i>Journal of Quality Technology</i><b>43</b>, 1–15, proposed a new class of designs called definitive screening designs. Definitive screening designs have more favourable properties than classical screening designs. In this paper, we study the projection properties of three-level screening designs. The comparison is based on several criteria such as D-efficiency, G-efficiency, A-efficiency and average of variance over a range of models that include main effects, interaction and quadratic terms. New designs are generated as projections of the full designs into a smaller factor dimensional space. The best projections and their properties are presented in a tabular form.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12306","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78239111","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: 3
Estimation of Poisson mean with under-reported counts: a double sampling approach 漏报计数的泊松均值估计:双重抽样方法
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-02-22 DOI: 10.1111/anzs.12308
Debjit Sengupta, Tathagata Banerjee, Surupa Roy
{"title":"Estimation of Poisson mean with under-reported counts: a double sampling approach","authors":"Debjit Sengupta,&nbsp;Tathagata Banerjee,&nbsp;Surupa Roy","doi":"10.1111/anzs.12308","DOIUrl":"10.1111/anzs.12308","url":null,"abstract":"<div>\u0000 \u0000 <p>Count data arising in various fields of applications are often under-reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood-based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12308","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81551963","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
The focussed information criterion for generalised linear regression models for time series 时间序列广义线性回归模型的集中信息准则
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-02-22 DOI: 10.1111/anzs.12310
S. C. Pandhare, T. V. Ramanathan
{"title":"The focussed information criterion for generalised linear regression models for time series","authors":"S. C. Pandhare,&nbsp;T. V. Ramanathan","doi":"10.1111/anzs.12310","DOIUrl":"10.1111/anzs.12310","url":null,"abstract":"<div>\u0000 \u0000 <p>The present paper proposes the focussed information criterion (FIC) to tackle the model selection problems pertinent to generalised linear models (GLM) for time series. As a first step towards constructing the FIC, we formally discuss the local asymptotic theory of quasi-maximum likelihood estimation for time series GLM under potential model misspecification. The general FIC formula is derived subsequently that is useful for the simultaneous selection of the order of the autoregressive response as well as a subset of important covariates. We also develop the average FIC (AFIC) that is instrumental in selecting an overall good model for a range of covariates and time regions and establish the equivalence of the AFIC with the classical Akaike's information criterion (AIC). We demonstrate our theory with the analysis of rainfall patterns in Melbourne by means of the logistic and Gamma regression models.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12310","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84139737","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
A loss-based prior for Gaussian graphical models 高斯图形模型的基于损失的先验
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-02-22 DOI: 10.1111/anzs.12307
Laurenţiu Cătălin Hinoveanu, Fabrizio Leisen, Cristiano Villa
{"title":"A loss-based prior for Gaussian graphical models","authors":"Laurenţiu Cătălin Hinoveanu,&nbsp;Fabrizio Leisen,&nbsp;Cristiano Villa","doi":"10.1111/anzs.12307","DOIUrl":"10.1111/anzs.12307","url":null,"abstract":"<div>\u0000 \u0000 <p>Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool, which allows one to describe the relationships among the variables of interest. From the Bayesian perspective, there are two sources of randomness: one is related to the multivariate distribution and the quantities that may parametrise the model, and the other has to do with the underlying graph, <i>G</i>, equivalent to describing the conditional independence structure of the model under consideration. In this paper, we propose a prior on <i>G</i> based on two loss components. One considers the loss in information one would incur in selecting the wrong graph, while the second penalises for large number of edges, favouring sparsity. We illustrate the prior on simulated data and on real datasets, and compare the results with other priors on <i>G</i> used in the literature. Moreover, we present a default choice of the prior as well as discuss how it can be calibrated so as to reflect available prior information.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12307","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89969461","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
Bayesian estimation and model comparison for linear dynamic panel models with missing values 缺失值线性动态面板模型的贝叶斯估计与模型比较
IF 1.1 4区 数学
Australian & New Zealand Journal of Statistics Pub Date : 2021-02-22 DOI: 10.1111/anzs.12316
Christian Aßmann, Marcel Preising
{"title":"Bayesian estimation and model comparison for linear dynamic panel models with missing values","authors":"Christian Aßmann,&nbsp;Marcel Preising","doi":"10.1111/anzs.12316","DOIUrl":"10.1111/anzs.12316","url":null,"abstract":"<p>Panel data are collected over several time periods for the same units and hence allow for modelling both latent heterogeneity and dynamics. Since in a dynamic setup, the dependent variable also appears as an explanatory variable in later periods, missing values lead to substantial loss of information and the possibility of inefficient estimation. For linear dynamic panel models with fixed or random effects, we suggest a Bayesian approach to deal with missing values. The Gibbs sampling scheme providing a sample from the posterior distribution is thereby augmented by draws from the full conditional distribution of the missing values. While the full conditional distribution for missing values in the dependent variable is implied by the model setup, we incorporate a flexible non-parametric approximation to the full conditional posterior distribution of missing values in the explaining variables. Also, we provide accurate non-nested model comparison in terms of the marginal likelihood from the resulting hybrid Gibbs sampling output. The properties and possible efficiency gains of the suggested approach are illustrated by means of a simulation study and an empirical application using a macroeconomic panel data set.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12316","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81016830","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}
引用次数: 3
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