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Optimality and constructions of spanning bipartite block designs 跨两方块设计的最优性和构造
IF 0.7 4区 数学
Metrika Pub Date : 2024-04-10 DOI: 10.1007/s00184-024-00963-3
Shoko Chisaki, Ryoh Fuji-Hara, Nobuko Miyamoto
{"title":"Optimality and constructions of spanning bipartite block designs","authors":"Shoko Chisaki, Ryoh Fuji-Hara, Nobuko Miyamoto","doi":"10.1007/s00184-024-00963-3","DOIUrl":"https://doi.org/10.1007/s00184-024-00963-3","url":null,"abstract":"<p>We consider a statistical problem to estimate variables (effects) that are associated with the edges of a complete bipartite graph <span>(K_{v_1, v_2}=(V_1, V_2;E))</span>. Each data is obtained as a sum of selected effects, a subset of <i>E</i>. To estimate efficiently, we propose a design called Spanning Bipartite Block Design (SBBD). For SBBDs such that the effects are estimable, we proved that the estimators have the same variance (variance balanced). If each block (a subgraph of <span>(K_{v_1, v_2})</span>) of SBBD is a semi-regular or a regular bipartite graph, we show that the design is A-optimum. We also show a construction of SBBD using an (<span>(r,lambda )</span>)-design and an ordered design. A BIBD with prime power blocks gives an A-optimum semi-regular or regular SBBD.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"84 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565961","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
Structure of hybrid censoring schemes and its implications 混合剔除方案的结构及其影响
IF 0.7 4区 数学
Metrika Pub Date : 2024-04-09 DOI: 10.1007/s00184-024-00960-6
Erhard Cramer
{"title":"Structure of hybrid censoring schemes and its implications","authors":"Erhard Cramer","doi":"10.1007/s00184-024-00960-6","DOIUrl":"https://doi.org/10.1007/s00184-024-00960-6","url":null,"abstract":"<p>In this paper, structural properties of (progressive) hybrid censoring schemes are established by studying the possible data scenarios resulting from the hybrid censoring scheme. The results illustrate that the distributions of hybrid censored random variables can be immediately derived from the cases of Type-I and Type-II censored data. Furthermore, it turns out that results in likelihood and Bayesian inference are also obtained directly which explains the similarities present in the probabilistic and statistical analysis of these censoring schemes. The power of the approach is illustrated by applying the approach to the quite complex unified Type-II (progressive) hybrid censoring scheme. Finally, it is shown that the approach is not restricted to (progressively Type-II censored) order statistics and that it can be extended to almost any kind of ordered data.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565959","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
Variance estimation for average treatment effects estimated by g-computation 通过 g 计算估计的平均治疗效果的方差估计
IF 0.7 4区 数学
Metrika Pub Date : 2024-04-06 DOI: 10.1007/s00184-024-00962-4
Stefan Nygaard Hansen, Morten Overgaard
{"title":"Variance estimation for average treatment effects estimated by g-computation","authors":"Stefan Nygaard Hansen, Morten Overgaard","doi":"10.1007/s00184-024-00962-4","DOIUrl":"https://doi.org/10.1007/s00184-024-00962-4","url":null,"abstract":"<p>The average treatment effect is used to evaluate effects of interventions in a population. Under certain causal assumptions, such an effect may be estimated from observational data using the g-computation technique. The asymptotic properties of this estimator appears not to be well-known and hence bootstrapping has become the preferred method for estimating its variance. Bootstrapping is, however, not an optimal choice for multiple reasons; it is a slow procedure and, if based on too few bootstrap samples, results in a highly variable estimator of the variance. In this paper, we consider estimators of potential outcome means and average treatment effects using g-computation. We consider these parameters for the entire population but also in subgroups, for example, the average treatment effect among the treated. We derive their asymptotic distributions in a general framework. An estimator of the asymptotic variance is proposed and shown to be consistent when g-computation is used in conjunction with the M-estimation technique. The proposed estimator is shown to be superior to the bootstrap technique in a simulation study. Robustness against model misspecification is also demonstrated by means of simulations.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565849","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
Estimating the suspected larger of two normal means 估计两个正态均值中较大的可疑值
IF 0.7 4区 数学
Metrika Pub Date : 2024-04-04 DOI: 10.1007/s00184-024-00961-5
Courtney Drew, Éric Marchand
{"title":"Estimating the suspected larger of two normal means","authors":"Courtney Drew, Éric Marchand","doi":"10.1007/s00184-024-00961-5","DOIUrl":"https://doi.org/10.1007/s00184-024-00961-5","url":null,"abstract":"<p>For <span>(X_1, X_2)</span> independently and normally distributed with means <span>(theta _1)</span> and <span>(theta _2)</span>, variances <span>(sigma ^2_1)</span> and <span>(sigma ^2_2)</span>, we consider Bayesian inference about <span>(theta _1)</span> with the difference <span>(theta _1-theta _2)</span> being lower-bounded by an uncertain <i>m</i>. We obtain a class of minimax Bayes estimators of <span>(theta _1)</span>, based on a posterior distribution for <span>((theta _1, theta _2)^{top })</span> taking values on <span>(mathbb {R}^2)</span>, which dominate the unrestricted MLE under squared error loss for <span>(theta _1-theta _2 ge 0)</span>. We also construct and study an ad hoc credible set for <span>(theta _1)</span> with approximate credibility <span>(1-alpha )</span> and provide numerical evidence of its frequentist coverage probability closely matching the nominal credibility level. A spending function is incorporated which further increases the coverage.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"74 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565848","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
Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean 自举绝对偏差中值的巴哈杜尔表示法及其在投影深度加权平均值中的应用
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-19 DOI: 10.1007/s00184-024-00958-0
Qing Liu, Xiaohui Liu, Zihao Hu
{"title":"Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean","authors":"Qing Liu, Xiaohui Liu, Zihao Hu","doi":"10.1007/s00184-024-00958-0","DOIUrl":"https://doi.org/10.1007/s00184-024-00958-0","url":null,"abstract":"<p>Median absolute deviation (hereafter MAD) is known as a robust alternative to the ordinary variance. It has been widely utilized to induce robust statistical inferential procedures. In this paper, we investigate the strong and weak Bahadur representations of its bootstrap counterpart. As a useful application, we utilize the results to derive the weak Bahadur representation of the bootstrap sample projection depth weighted mean—a quite important location estimator depending on MAD.\u0000</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168772","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
Measures of kurtosis: inadmissible for asymmetric distributions? 峰度测量：非对称分布不允许？
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-17 DOI: 10.1007/s00184-024-00959-z
Andreas Eberl, Bernhard Klar
{"title":"Measures of kurtosis: inadmissible for asymmetric distributions?","authors":"Andreas Eberl, Bernhard Klar","doi":"10.1007/s00184-024-00959-z","DOIUrl":"https://doi.org/10.1007/s00184-024-00959-z","url":null,"abstract":"<p>Skewness and kurtosis are natural characteristics of a distribution. While it has long been recognized that they are more intrinsically entangled than other characteristics like location and dispersion, this has recently been made more explicit by Eberl and Klar (Stat Papers 65:415–433, 2024) with regard to orders of kurtosis. In this paper, we analyze the implications of this entanglement on kurtosis measures in general and for several specific examples. As a key finding, we show that kurtosis measures that are defined in the classical order-based way, which is analogous to measures of location, dispersion and skewness, do not exist. This raises serious doubts about the frequent application of such measures to skewed data. We then consider old and new proposals for kurtosis measures and evaluate under which additional conditions they measure kurtosis in a meaningful way. Some measures also allow more specific representations of the influence of skewness on the measurement of kurtosis than are available in a general setting. This works particularly well for a family of newly introduced density-based kurtosis measures.\u0000</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"2013 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156658","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
Staged trees and asymmetry-labeled DAGs 分期树和不对称标记的 DAG
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-07 DOI: 10.1007/s00184-024-00957-1
Gherardo Varando, Federico Carli, Manuele Leonelli
{"title":"Staged trees and asymmetry-labeled DAGs","authors":"Gherardo Varando, Federico Carli, Manuele Leonelli","doi":"10.1007/s00184-024-00957-1","DOIUrl":"https://doi.org/10.1007/s00184-024-00957-1","url":null,"abstract":"<p>Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they can be seen as a special case of the much more general class of models called staged trees, which can represent any non-symmetric conditional independence. Here we formalize the relationship between these two models and introduce a minimal Bayesian network representation of a staged tree, which can be used to read conditional independences intuitively. A new labeled graph termed asymmetry-labeled directed acyclic graph is defined, with edges labeled to denote the type of dependence between any two random variables. We also present a novel algorithm to learn staged trees which only enforces a specific subset of non-symmetric independences. Various datasets illustrate the methodology, highlighting the need to construct models that more flexibly encode and represent non-symmetric structures.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075893","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
Right-censored nonparametric regression with measurement error 有测量误差的右删失非参数回归
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-05 DOI: 10.1007/s00184-024-00953-5
Dursun Aydın, Ersin Yılmaz, Nur Chamidah, Budi Lestari, I. Nyoman Budiantara
{"title":"Right-censored nonparametric regression with measurement error","authors":"Dursun Aydın, Ersin Yılmaz, Nur Chamidah, Budi Lestari, I. Nyoman Budiantara","doi":"10.1007/s00184-024-00953-5","DOIUrl":"https://doi.org/10.1007/s00184-024-00953-5","url":null,"abstract":"<p>This study focuses on estimating a nonparametric regression model with right-censored data when the covariate is subject to measurement error. To achieve this goal, it is necessary to solve the problems of censorship and measurement error ignored by many researchers. Note that the presence of measurement errors causes biased and inconsistent parameter estimates. Moreover, non-parametric regression techniques cannot be applied directly to right-censored observations. In this context, we consider an updated response variable using the Buckley–James method (BJM), which is essentially based on the Kaplan–Meier estimator, to solve the censorship problem. Then the measurement error problem is handled using the kernel deconvolution method, which is a specialized tool to solve this problem. Accordingly, three denconvoluted estimators based on BJM are introduced using kernel smoothing, local polynomial smoothing, and B-spline techniques that incorporate both the updated response variable and kernel deconvolution.The performances of these estimators are compared in a detailed simulation study. In addition, a real-world data example is presented using the Covid-19 dataset.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"32 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140043951","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
Bootstrap for inference after model selection and model averaging for likelihood models 模型选择后的推理引导和似然模型的模型平均法
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-05 DOI: 10.1007/s00184-024-00956-2
Andrea C. Garcia-Angulo, Gerda Claeskens
{"title":"Bootstrap for inference after model selection and model averaging for likelihood models","authors":"Andrea C. Garcia-Angulo, Gerda Claeskens","doi":"10.1007/s00184-024-00956-2","DOIUrl":"https://doi.org/10.1007/s00184-024-00956-2","url":null,"abstract":"<p>A one-step semiparametric bootstrap procedure is constructed to estimate the distribution of estimators after model selection and of model averaging estimators with data-dependent weights. The method is generally applicable to non-normal models. Misspecification is allowed for all candidate parametric models. The semiparametric bootstrap estimator is shown to be consistent within specific regions such that the good and the bad candidate models are separated. Simulation studies exemplify that the bootstrap procedure leads to short confidence intervals with a good coverage.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"156 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140043940","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 some properties of one nonparametric estimate of poisson regression function 关于泊松回归函数的一种非参数估计的一些特性
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-01 DOI: 10.1007/s00184-024-00955-3
P. Babilua, E. Nadaraya
{"title":"On some properties of one nonparametric estimate of poisson regression function","authors":"P. Babilua, E. Nadaraya","doi":"10.1007/s00184-024-00955-3","DOIUrl":"https://doi.org/10.1007/s00184-024-00955-3","url":null,"abstract":"<p>The paper considers the nonparametric Poisson regression problem with a regular equidistant design on the unit interval. The nonparametric estimation of the Poisson regression function is studied. The uniform consistency conditions are established and the limit theorems are proved for continuous functionals on <span>(C[a,1-a])</span>, <span>(0&lt;a&lt;frac{1}{2})</span> .</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"15 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019158","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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