{"title":"On the mean perimeter density of inhomogeneous random closed sets","authors":"Elena Villa","doi":"10.3150/22-bej1558","DOIUrl":"https://doi.org/10.3150/22-bej1558","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48689905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01Epub Date: 2023-08-22DOI: 10.3150/22-bej1565
Xiangbin Hu, L I Liu, Ying Zhang, Xingqiu Zhao
We study a semiparametric model for robust analysis of panel count data with an informative terminal event. To explore the explicit effect of the terminal event on recurrent events of interest, we propose a conditional mean model for a reversed counting process anchoring at the terminal event. Treating the distribution function of the terminal event as a nuisance functional parameter, we develop a predicted least squares-based two-stage estimation procedure with the spline-based sieve estimation technique, and derive the convergence rate of the proposed estimator. Furthermore, overcoming the difficulties caused by the convergence rate slower than , we establish the asymptotic normality for the estimator of the finite-dimensional parameter and a functional of the estimator of the infinite-dimensional parameter. The proposed method is evaluated through extensive simulation studies and illustrated with an application to the Longitudinal Healthy Longevity Survey study on elder people in China.
{"title":"Semiparametric regression of panel count data with informative terminal event.","authors":"Xiangbin Hu, L I Liu, Ying Zhang, Xingqiu Zhao","doi":"10.3150/22-bej1565","DOIUrl":"10.3150/22-bej1565","url":null,"abstract":"<p><p>We study a semiparametric model for robust analysis of panel count data with an informative terminal event. To explore the explicit effect of the terminal event on recurrent events of interest, we propose a conditional mean model for a reversed counting process anchoring at the terminal event. Treating the distribution function of the terminal event as a nuisance functional parameter, we develop a predicted least squares-based two-stage estimation procedure with the spline-based sieve estimation technique, and derive the convergence rate of the proposed estimator. Furthermore, overcoming the difficulties caused by the convergence rate slower than <math><mrow><mn>1</mn> <mo>∕</mo> <msqrt><mi>n</mi></msqrt> </mrow> </math> , we establish the asymptotic normality for the estimator of the finite-dimensional parameter and a functional of the estimator of the infinite-dimensional parameter. The proposed method is evaluated through extensive simulation studies and illustrated with an application to the Longitudinal Healthy Longevity Survey study on elder people in China.</p>","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":"2828-2853"},"PeriodicalIF":1.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12040413/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41555591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper establishes necessary and sufficient conditions for the asymptotic normality of higher order Turing estimators. It further gives several easy to verify sufficient conditions. These conditions are then used to show that the assumptions hold for large classes of distributions with regularly varying tails. This includes classes for which asymptotic normality had not been previously verified.
{"title":"Necessary and sufficient conditions for the asymptotic normality of higher order Turing estimators","authors":"Jie Chang, Michael Grabchak","doi":"10.3150/23-bej1587","DOIUrl":"https://doi.org/10.3150/23-bej1587","url":null,"abstract":"This paper establishes necessary and sufficient conditions for the asymptotic normality of higher order Turing estimators. It further gives several easy to verify sufficient conditions. These conditions are then used to show that the assumptions hold for large classes of distributions with regularly varying tails. This includes classes for which asymptotic normality had not been previously verified.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":"1055 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136172321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bootstrap inference in functional linear regression models with scalar response","authors":"Hyemin Yeon, Xiongtao Dai, D. Nordman","doi":"10.3150/22-bej1554","DOIUrl":"https://doi.org/10.3150/22-bej1554","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42658635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. G. González Cázares, A. Kohatsu-Higa, A. Mijatović
{"title":"Joint density of the stable process and its supremum: Regularity and upper bounds","authors":"J. G. González Cázares, A. Kohatsu-Higa, A. Mijatović","doi":"10.3150/23-bej1590","DOIUrl":"https://doi.org/10.3150/23-bej1590","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45286231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cramér type moderate deviations for the Grenander estimator near the boundaries of the support","authors":"F. Gao, Hui Jiang, Xingqiu Zhao","doi":"10.3150/22-bej1566","DOIUrl":"https://doi.org/10.3150/22-bej1566","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43132086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Additive regression with parametric help","authors":"H. Hong, Young K. Lee, Byeong-U Park","doi":"10.3150/22-bej1575","DOIUrl":"https://doi.org/10.3150/22-bej1575","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49551018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Luciano de Castro, Bruno N. Costa, Antonio F. Galvao, Jorge P. Zubelli
This paper derives several novel properties of conditional quantiles viewed as nonlinear operators. The results are organized in parallel to the usual properties of the expectation operator. We first define a τ-conditional quantile random set, relative to any sigma-algebra, as a set of solutions of an optimization problem. Then, well-known properties of unconditional quantiles, as translation invariance, comonotonicity, and equivariance to monotone transformations, are generalized to the conditional case. Moreover, a simple proof for Jensen’s inequality for conditional quantiles is provided. We also investigate continuity of conditional quantiles as operators with respect to different topologies and obtain a novel Fatou’s lemma for quantiles. Conditions for continuity in Lp and weak continuity are also derived. Then, the differentiability properties of quantiles are addressed. We demonstrate the validity of Leibniz’s rule for conditional quantiles for the cases of monotone, as well as separable functions. Finally, although the law of iterated quantiles does not hold in general, we characterize the maximum set of random variables for which this law holds, and investigate its consequences for the infinite composition of conditional quantiles.
{"title":"Conditional quantiles: An operator-theoretical approach","authors":"Luciano de Castro, Bruno N. Costa, Antonio F. Galvao, Jorge P. Zubelli","doi":"10.3150/22-bej1546","DOIUrl":"https://doi.org/10.3150/22-bej1546","url":null,"abstract":"This paper derives several novel properties of conditional quantiles viewed as nonlinear operators. The results are organized in parallel to the usual properties of the expectation operator. We first define a τ-conditional quantile random set, relative to any sigma-algebra, as a set of solutions of an optimization problem. Then, well-known properties of unconditional quantiles, as translation invariance, comonotonicity, and equivariance to monotone transformations, are generalized to the conditional case. Moreover, a simple proof for Jensen’s inequality for conditional quantiles is provided. We also investigate continuity of conditional quantiles as operators with respect to different topologies and obtain a novel Fatou’s lemma for quantiles. Conditions for continuity in Lp and weak continuity are also derived. Then, the differentiability properties of quantiles are addressed. We demonstrate the validity of Leibniz’s rule for conditional quantiles for the cases of monotone, as well as separable functions. Finally, although the law of iterated quantiles does not hold in general, we characterize the maximum set of random variables for which this law holds, and investigate its consequences for the infinite composition of conditional quantiles.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135516896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stability of the Poincaré constant","authors":"Serres Jordan","doi":"10.3150/22-bej1499","DOIUrl":"https://doi.org/10.3150/22-bej1499","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47785827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article investigates whether time-varying quantile regression curves are the same up to the horizontal shift or not. The errors and the covariates involved in the regression model are allowed to be locally stationary. We formalize this issue in a corresponding non-parametric hypothesis testing problem, and develop an integrated-squared-norm based test (SIT) as well as a simultaneous confidence band (SCB) approach. The asymptotic properties of SIT and SCB under null and local alternatives are derived. Moreover, the asymptotic properties of these tests are also studied when the compared data sets are dependent. We then propose valid wild bootstrap algorithms to implement SIT and SCB. Furthermore, the usefulness of the proposed methodology is illustrated via analysing simulated and real data related to COVID-19 outbreak and climate science. bootstrap, comparison of curves, confidence band, hypothesis testing, locally stationary process, nonparametric quantile regression, COVID-19. 1 ar X iv :2 01 1. 06 33 3v 2 [ st at .M E ] 2 4 D ec 2 02 1
本文研究了时变分位数回归曲线在水平位移之前是否相同。回归模型中涉及的误差和协变量被允许是局部平稳的。我们将这个问题形式化为相应的非参数假设检验问题，并开发了一种基于平方范数的综合检验（SIT）和同时置信带（SCB）方法。导出了SIT和SCB在零和局部替换下的渐近性质。此外，当比较的数据集是相依的时，还研究了这些检验的渐近性质。然后，我们提出了有效的野生自举算法来实现SIT和SCB。此外，通过分析与新冠肺炎疫情和气候科学相关的模拟和真实数据，说明了拟议方法的有用性。bootstrap、曲线比较、置信区间、假设检验、局部平稳过程、非参数分位数回归、新冠肺炎。1 ar X iv：2 01 1。06 33 3v 2[st at.M E]2 4 D ec 2 02 1
{"title":"Comparing time varying regression quantiles under shift invariance","authors":"S. S. Dhar, Weichi Wu","doi":"10.3150/22-bej1509","DOIUrl":"https://doi.org/10.3150/22-bej1509","url":null,"abstract":"This article investigates whether time-varying quantile regression curves are the same up to the horizontal shift or not. The errors and the covariates involved in the regression model are allowed to be locally stationary. We formalize this issue in a corresponding non-parametric hypothesis testing problem, and develop an integrated-squared-norm based test (SIT) as well as a simultaneous confidence band (SCB) approach. The asymptotic properties of SIT and SCB under null and local alternatives are derived. Moreover, the asymptotic properties of these tests are also studied when the compared data sets are dependent. We then propose valid wild bootstrap algorithms to implement SIT and SCB. Furthermore, the usefulness of the proposed methodology is illustrated via analysing simulated and real data related to COVID-19 outbreak and climate science. bootstrap, comparison of curves, confidence band, hypothesis testing, locally stationary process, nonparametric quantile regression, COVID-19. 1 ar X iv :2 01 1. 06 33 3v 2 [ st at .M E ] 2 4 D ec 2 02 1","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46907323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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