{"title":"Central limit theorems for semi-discrete Wasserstein distances","authors":"E. del Barrio, Alberto González Sanz, J. Loubes","doi":"10.3150/23-bej1608","DOIUrl":"https://doi.org/10.3150/23-bej1608","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139685217","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":"Semiparametric regression of panel count data with informative terminal event","authors":"Xiangbin Hu, Li Liu, Ying Zhang, Xingqiu Zhao","doi":"10.3150/22-bej1565","DOIUrl":"https://doi.org/10.3150/22-bej1565","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"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":null,"pages":null},"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}
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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