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A proper selection among multiple Buckley–James estimates 从多个巴克利-詹姆斯估计值中进行适当选择
IF 0.7 4区 数学
Metrika Pub Date : 2023-12-14 DOI: 10.1007/s00184-023-00933-1
Qiqing Yu
{"title":"A proper selection among multiple Buckley–James estimates","authors":"Qiqing Yu","doi":"10.1007/s00184-023-00933-1","DOIUrl":"https://doi.org/10.1007/s00184-023-00933-1","url":null,"abstract":"<p>Consider the semiparametric linear regression estimation problem with right-censored data. Under right censoring, the Buckley–James estimator (BJE) is the standard extension of the least squares estimator. Moreover, an iterative algorithm for the BJE has been implemented in R package called rms. We show that it often does not yield a solution, even if a consistent BJE exists. Yu and Wong (J Stat Comput Simul 72:451–460, 2002) proposed another algorithm to find all possible BJEs. The latter algorithm is modified in this paper so that it indeed finds all BJEs when the underlying regression parameter vector is identifiable. We show that some of these BJE’s can be inconsistent. Thus it is important to decide how to select a proper BJE such that it is consistent if the parameter is identifiable. We suggest either choose one close to the modified semi-parametric maximum likelihood estimator (Yu and Wong in Technometrics 47:34–42, 2005) or a finite boundary point if there are infinitely many BJEs.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629798","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
Modelling and diagnostic tests for Poisson and negative-binomial count time series 泊松和负二项计数时间序列的建模和诊断检测
IF 0.7 4区 数学
Metrika Pub Date : 2023-12-13 DOI: 10.1007/s00184-023-00934-0
Boris Aleksandrov, Christian H. Weiß, Simon Nik, Maxime Faymonville, Carsten Jentsch
{"title":"Modelling and diagnostic tests for Poisson and negative-binomial count time series","authors":"Boris Aleksandrov, Christian H. Weiß, Simon Nik, Maxime Faymonville, Carsten Jentsch","doi":"10.1007/s00184-023-00934-0","DOIUrl":"https://doi.org/10.1007/s00184-023-00934-0","url":null,"abstract":"<p>When modelling unbounded counts, their marginals are often assumed to follow either Poisson (Poi) or negative binomial (NB) distributions. To test such null hypotheses, we propose goodness-of-fit (GoF) tests based on statistics relying on certain moment properties. By contrast to most approaches proposed in the count-data literature so far, we do not restrict ourselves to specific low-order moments, but consider a flexible class of functions of generalized moments to construct model-diagnostic tests. These cover GoF-tests based on higher-order factorial moments, which are particularly suitable for the Poi- or NB-distribution where simple closed-form expressions for factorial moments of any order exist, but also GoF-tests relying on the respective Stein’s identity for the Poi- or NB-distribution. In the time-dependent case, under mild mixing conditions, we derive the asymptotic theory for GoF tests based on higher-order factorial moments for a wide family of stationary processes having Poi- or NB-marginals, respectively. This family also includes a type of NB-autoregressive model, where we provide clarification of some confusion caused in the literature. Additionally, for the case of independent and identically distributed counts, we prove asymptotic normality results for GoF-tests relying on a Stein identity, and we briefly discuss how its statistic might be used to define an omnibus GoF-test. The performance of the tests is investigated with simulations for both asymptotic and bootstrap implementations, also considering various alternative scenarios for power analyses. A data example of daily counts of downloads of a TeX editor is used to illustrate the application of the proposed GoF-tests.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629803","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
Jackknife model averaging for mixed-data kernel-weighted spline quantile regressions 混合数据核加权样条分位数回归的折刀模型平均
IF 0.7 4区 数学
Metrika Pub Date : 2023-11-28 DOI: 10.1007/s00184-023-00932-2
Xianwen Sun, Lixin Zhang
{"title":"Jackknife model averaging for mixed-data kernel-weighted spline quantile regressions","authors":"Xianwen Sun, Lixin Zhang","doi":"10.1007/s00184-023-00932-2","DOIUrl":"https://doi.org/10.1007/s00184-023-00932-2","url":null,"abstract":"<p>In the past two decades, model averaging has attracted more and more attention and is regarded as a much better tool to solve model uncertainty than model selection. Compared with the conditional mean regression, the quantile regression serves as a robust alternative and shows a lot more information about the conditional distribution of a response variable. In this paper, we propose a jackknife model averaging procedure that chooses the weights by minimizing a leave-one-out cross-validation criterion function for mixed-data kernel-weighted spline quantile regressions that contain both continuous and categorical regressors when all candidate models are potentially misspecified. We demonstrate the JMA estimator is asymptotically optimal in terms of minimizing the out-of-sample final prediction error. Simulation experiments are conducted to assess the relative finite-sample performance of the proposed JMA method with respect to other model selection and averaging methods. Our JMA method is applied to the wage and house datasets.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515265","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
Cumulative information generating function and generalized Gini functions 累积信息生成函数与广义基尼函数
IF 0.7 4区 数学
Metrika Pub Date : 2023-11-27 DOI: 10.1007/s00184-023-00931-3
Marco Capaldo, Antonio Di Crescenzo, Alessandra Meoli
{"title":"Cumulative information generating function and generalized Gini functions","authors":"Marco Capaldo, Antonio Di Crescenzo, Alessandra Meoli","doi":"10.1007/s00184-023-00931-3","DOIUrl":"https://doi.org/10.1007/s00184-023-00931-3","url":null,"abstract":"<p>We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival function. Specifically, after establishing its main properties and some bounds, we show that it is a variability measure itself that extends the Gini mean semi-difference. We also provide (i) an extension of such a measure, based on distortion functions, and (ii) a weighted version based on a mixture distribution. Furthermore, we explore some connections with the reliability of <i>k</i>-out-of-<i>n</i> systems and with stress–strength models for multi-component systems. Also, we address the problem of extending the cumulative information generating function to higher dimensions.\u0000</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515264","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
Stochastic comparisons of two finite mixtures of general family of distributions 一般分布族的两个有限混合的随机比较
IF 0.7 4区 数学
Metrika Pub Date : 2023-11-20 DOI: 10.1007/s00184-023-00930-4
Raju Bhakta, Priyanka Majumder, Suchandan Kayal, Narayanaswamy Balakrishnan
{"title":"Stochastic comparisons of two finite mixtures of general family of distributions","authors":"Raju Bhakta, Priyanka Majumder, Suchandan Kayal, Narayanaswamy Balakrishnan","doi":"10.1007/s00184-023-00930-4","DOIUrl":"https://doi.org/10.1007/s00184-023-00930-4","url":null,"abstract":"<p>We consider here two finite (arithmetic) mixture models (FMMs) with general parametric family of distributions. Sufficient conditions for the usual stochastic order and hazard rate order are then established under the assumption that the model parameter vectors are connected in <i>p</i>-larger order, reciprocal majorization order and weak super/sub majorization order. Furthermore, we establish hazard rate order and reversed hazard rate order between two mixture random variables (MRVs) when a matrix of model parameters and mixing proportions changes to another matrix in some mathematical sense. We have also considered scale family of distributions to establish some sufficient conditions under which the MRVs have hazard rate order. Several examples are presented to illustrate and clarify all the results established here.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542759","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 multivariate nonlinear mixed models for censored longitudinal trajectories with non-monotone missing values 具有非单调缺失值的截尾纵向轨迹的贝叶斯多元非线性混合模型
4区 数学
Metrika Pub Date : 2023-10-26 DOI: 10.1007/s00184-023-00929-x
Wan-Lun Wang, Luis M. Castro, Tsung-I Lin
{"title":"Bayesian multivariate nonlinear mixed models for censored longitudinal trajectories with non-monotone missing values","authors":"Wan-Lun Wang, Luis M. Castro, Tsung-I Lin","doi":"10.1007/s00184-023-00929-x","DOIUrl":"https://doi.org/10.1007/s00184-023-00929-x","url":null,"abstract":"","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134909468","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
On the asymptotic behaviour of the joint distribution of the maxima and minima of observations, when the sample size is a random variable 当样本量为随机变量时，观测值的最大值和最小值的联合分布的渐近性态
4区 数学
Metrika Pub Date : 2023-10-17 DOI: 10.1007/s00184-023-00928-y
R. Vasudeva
{"title":"On the asymptotic behaviour of the joint distribution of the maxima and minima of observations, when the sample size is a random variable","authors":"R. Vasudeva","doi":"10.1007/s00184-023-00928-y","DOIUrl":"https://doi.org/10.1007/s00184-023-00928-y","url":null,"abstract":"","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135995572","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 ridge prediction error sum of squares statistic in linear mixed models 线性混合模型中脊预测误差平方和统计量
4区 数学
Metrika Pub Date : 2023-10-05 DOI: 10.1007/s00184-023-00927-z
Özge Kuran, M. Revan Özkale
{"title":"The ridge prediction error sum of squares statistic in linear mixed models","authors":"Özge Kuran, M. Revan Özkale","doi":"10.1007/s00184-023-00927-z","DOIUrl":"https://doi.org/10.1007/s00184-023-00927-z","url":null,"abstract":"","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134974921","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
Large deviations for randomly weighted least squares estimator in a nonlinear regression model 非线性回归模型中随机加权最小二乘估计量的大偏差
4区 数学
Metrika Pub Date : 2023-10-04 DOI: 10.1007/s00184-023-00926-0
Yi Wu, Wei Yu, Xuejun Wang
{"title":"Large deviations for randomly weighted least squares estimator in a nonlinear regression model","authors":"Yi Wu, Wei Yu, Xuejun Wang","doi":"10.1007/s00184-023-00926-0","DOIUrl":"https://doi.org/10.1007/s00184-023-00926-0","url":null,"abstract":"","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135592330","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
Second-order (s.o.) multi-stage fixed-width confidence interval (FWCI) estimation strategies for comparing location parameters from two negative exponential (NE) populations: illustrations with cancer data 二阶(s.o)多阶段固定宽度置信区间(FWCI)估计策略，用于比较两个负指数(NE)种群的位置参数:癌症数据的插图
4区 数学
Metrika Pub Date : 2023-10-01 DOI: 10.1007/s00184-023-00925-1
Nitis Mukhopadhyay, Anhar Aloufi
{"title":"Second-order (s.o.) multi-stage fixed-width confidence interval (FWCI) estimation strategies for comparing location parameters from two negative exponential (NE) populations: illustrations with cancer data","authors":"Nitis Mukhopadhyay, Anhar Aloufi","doi":"10.1007/s00184-023-00925-1","DOIUrl":"https://doi.org/10.1007/s00184-023-00925-1","url":null,"abstract":"","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135407010","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
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