Australian & New Zealand Journal of Statistics最新文献_第8页

Odds-symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables 平方列联表中累积概率的奇数-对称模型及条件对称模型的分解

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-12-06 DOI: 10.1111/anzs.12346

Shuji Ando

{"title":"Odds-symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables","authors":"Shuji Ando","doi":"10.1111/anzs.12346","DOIUrl":"10.1111/anzs.12346","url":null,"abstract":"<div>\u0000 \u0000 For the analysis of square contingency tables, it is necessary to estimate an unknown distribution with high confidence from an obtained observation. For that purpose, we need to introduce a statistical model that fits the data well and has parsimony. This study proposes asymmetry models based on cumulative probabilities for square contingency tables with the same row and column ordinal classifications. In the proposed models, the odds, for all i<j, that an observation will fall in row category i or below, and column category j or above, instead of row category j or above, and column category i or below, depend on only row category i or column category j. This is notwithstanding that the odds are constant without relying on row and column categories under the conditional symmetry (CS) model. The proposed models constantly hold when the CS model holds. However, the converse is not necessarily true. This study also shows that it is necessary to satisfy the extended marginal homogeneity model, in addition to the proposed models, to satisfy the CS model. These decomposition theorems explain why the CS model does not hold. The proposed models provide a better fit for application to a single data set of real-world occupational data for father-and-son dyads.\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 4","pages":"674-684"},"PeriodicalIF":1.1,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77244237","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

Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data 比例反高斯分布:分析连续比例数据的新工具

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-23 DOI: 10.1111/anzs.12345

Pengyi Liu, Guo-Liang Tian, Kam Chuen Yuen, Chi Zhang, Man-Lai Tang

{"title":"Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data","authors":"Pengyi Liu, Guo-Liang Tian, Kam Chuen Yuen, Chi Zhang, Man-Lai Tang","doi":"10.1111/anzs.12345","DOIUrl":"10.1111/anzs.12345","url":null,"abstract":"<div>\u0000 \u0000 Outcomes in the form of rates, fractions, proportions and percentages often appear in various fields. Existing beta and simplex distributions are frequently unable to exhibit satisfactory performances in fitting such continuous data. This paper aims to develop the normalised inverse Gaussian (N-IG) distribution proposed by Lijoi, Mena & Prünster (2005, Journal of the American Statistical Association, 100, 1278–1291) as a new tool for analysing continuous proportional data in (0,1) and renames the N-IG as proportional inverse Gaussian (PIG) distribution. Our main contributions include: (i) To overcome the difficulty of an integral in the PIG density function, we propose a novel minorisation–maximisation (MM) algorithm via the continuous version of Jensen's inequality to calculate the maximum likelihood estimates of the parameters in the PIG distribution; (ii) We also develop an MM algorithm aided by the gradient descent algorithm for the PIG regression model, which allows us to explore the relationship between a set of covariates with the mean parameter; (iii) Both the comparative studies and the real data analyses show that the PIG distribution is better when comparing with the beta and simplex distributions in terms of the AIC, the Cramér–von Mises and the Kolmogorov–Smirnov tests. In addition, bootstrap confidence intervals and testing hypothesis on the symmetry of the PIG density are also presented. Simulation studies are conducted and the hospital stay data of Barcelona in 1988 and 1990 are analysed to illustrate the proposed methods.\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 4","pages":"579-605"},"PeriodicalIF":1.1,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87974708","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

BNPdensity: Bayesian nonparametric mixture modelling in R bnp密度:贝叶斯非参数混合建模

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-17 DOI: 10.1111/anzs.12342

J. Arbel, G. Kon Kam King, A. Lijoi, L. Nieto-Barajas, I. Prünster

{"title":"BNPdensity: Bayesian nonparametric mixture modelling in R","authors":"J. Arbel, G. Kon Kam King, A. Lijoi, L. Nieto-Barajas, I. Prünster","doi":"10.1111/anzs.12342","DOIUrl":"10.1111/anzs.12342","url":null,"abstract":"<div>\u0000 \u0000 Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of parameters. The aim of this work is to facilitate the journey by providing computational tools for Bayesian nonparametric inference. The article describes a set of functions available in the R package BNPdensity in order to carry out density estimation with an infinite mixture model, including all types of censored data. The package provides access to a large class of such models based on normalised random measures, which represent a generalisation of the popular Dirichlet process mixture. One striking advantage of this generalisation is that it offers much more robust priors on the number of clusters than the Dirichlet. Another crucial advantage is the complete flexibility in specifying the prior for the scale and location parameters of the clusters, because conjugacy is not required. Inference is performed using a theoretically grounded approximate sampling methodology known as the Ferguson & Klass algorithm. The package also offers several goodness-of-fit diagnostics such as QQ plots, including a cross-validation criterion, the conditional predictive ordinate. The proposed methodology is illustrated on a classical ecological risk assessment method called the species sensitivity distribution problem, showcasing the benefits of the Bayesian nonparametric framework.\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 3","pages":"542-564"},"PeriodicalIF":1.1,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90676545","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

Experimental design in practice: The importance of blocking and treatment structures 实践中的实验设计:阻塞和处理结构的重要性

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-08 DOI: 10.1111/anzs.12343

E.R. Williams, C.G. Forde, J. Imaki, K. Oelkers

引用次数: 1

Accelerating adaptation in the adaptive Metropolis–Hastings random walk algorithm 自适应Metropolis-Hastings随机漫步算法中的加速自适应

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-03 DOI: 10.1111/anzs.12344

Simon E.F. Spencer

引用次数: 6

Variable selection using penalised likelihoods for point patterns on a linear network 使用惩罚似然对线性网络上的点模式进行变量选择

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-10-18 DOI: 10.1111/anzs.12341

Suman Rakshit, Greg McSwiggan, Gopalan Nair, Adrian Baddeley

{"title":"Variable selection using penalised likelihoods for point patterns on a linear network","authors":"Suman Rakshit, Greg McSwiggan, Gopalan Nair, Adrian Baddeley","doi":"10.1111/anzs.12341","DOIUrl":"10.1111/anzs.12341","url":null,"abstract":"<div>\u0000 \u0000 Motivated by the analysis of a comprehensive database of road traffic accidents, we investigate methods of variable selection for spatial point process models on a linear network. The original data may include explanatory spatial covariates, such as road curvature, and ‘mark’ variables attributed to individual accidents, such as accident severity. The treatment of mark variables is new. Variable selection is applied to the canonical covariates, which may include spatial covariate effects, mark effects and mark-covariate interactions. We approximate the likelihood of the point process model by that of a generalised linear model, in such a way that spatial covariates and marks are both associated with canonical covariates. We impose a convex penalty on the log likelihood, principally the elastic-net penalty, and maximise the penalised loglikelihood by cyclic coordinate ascent. A simulation study compares the performances of the lasso, ridge regression and elastic-net methods of variable selection on their ability to select variables correctly, and on their bias and standard error. Standard techniques for selecting the regularisation parameter γ often yielded unsatisfactory results. We propose two new rules for selecting γ which are designed to have better performance. The methods are tested on a small dataset on crimes in a Chicago neighbourhood, and applied to a large dataset of road traffic accidents in Western Australia.\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 3","pages":"417-454"},"PeriodicalIF":1.1,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90533201","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

ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density 用ECM算法估计具有方差分布和可能无界密度的向量ARMA模型

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-10-18 DOI: 10.1111/anzs.12340

Thanakorn Nitithumbundit, Jennifer S.K. Chan

{"title":"ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density","authors":"Thanakorn Nitithumbundit, Jennifer S.K. Chan","doi":"10.1111/anzs.12340","DOIUrl":"https://doi.org/10.1111/anzs.12340","url":null,"abstract":"<div>\u0000 \u0000 The simultaneous analysis of several financial time series is salient in portfolio setting and risk management. This paper proposes a novel alternating expectation conditional maximisation (AECM) algorithm to estimate the vector autoregressive moving average (VARMA) model with variance gamma (VG) error distribution in the multivariate skewed setting. We explain why the VARMA-VG model is suitable for high-frequency returns (HFRs) because VG distribution provides thick tails to capture the high kurtosis in the data and unbounded central density further captures the majority of near-zero HFRs. The distribution can also be expressed in normal-mean-variance mixtures to facilitate model implementation using the Bayesian or expectation maximisation (EM) approach. We adopt the EM approach to avoid the time-consuming Markov chain Monto Carlo sampling and solve the unbounded density problem in the classical maximum likelihood estimation. We conduct extensive simulation studies to evaluate the accuracy of the proposed AECM estimator and apply the models to analyse the dependency between two HFR series from the time zones that only differ by one hour.\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 3","pages":"485-516"},"PeriodicalIF":1.1,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137538704","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

The Inverse G-Wishart distribution and variational message passing 逆G-Wishart分布与变分消息传递

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-10-07 DOI: 10.1111/anzs.12339

Luca Maestrini, Matt P. Wand

引用次数: 5

An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture-based clustering 基于OTRIMLE鲁棒高斯混合聚类的聚类数量决定的充分性方法

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-09-03 DOI: 10.1111/anzs.12338

Christian Hennig, Pietro Coretto

{"title":"An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture-based clustering","authors":"Christian Hennig, Pietro Coretto","doi":"10.1111/anzs.12338","DOIUrl":"10.1111/anzs.12338","url":null,"abstract":"We introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto & Hennig, Journal of the American Statistical Association 111, 1648–1659) of a Gaussian mixture model allowing for observations to be classified as ‘noise’, but it can be applied to other clustering methods as well. The quality of a clustering is assessed by a statistic Q that measures how close the within-cluster distributions are to elliptical unimodal distributions that have the only mode in the mean. This non-parametric measure allows for non-Gaussian clusters as long as they have a good quality according to Q. The simplicity of a model is assessed by a measure S that prefers a smaller number of clusters unless additional clusters can reduce the estimated noise proportion substantially. The simplest model is then chosen that is adequate for the data in the sense that its observed value of Q is not significantly larger than what is expected for data truly generated from the fitted model, as can be assessed by parametric bootstrap. The approach is compared with model-based clustering using the Bayesian information criterion (BIC) and the integrated complete likelihood (ICL) in a simulation study and on two real data sets.","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"64 2","pages":"230-254"},"PeriodicalIF":1.1,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12338","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75692546","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

What is the effective sample size of a spatial point process? 空间点过程的有效样本量是多少?

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-07-21 DOI: 10.1111/anzs.12337

Ian W. Renner, David I. Warton, Francis K.C. Hui

引用次数: 4