The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the...The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.展开更多
In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergen...In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.展开更多
Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+...Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.展开更多
In this paper,the author obtains complete convergence for the maximum partial sums of m-widely orthant dependent(m-WOD)random variables sequences under some general conditions.The results extend the complete convergen...In this paper,the author obtains complete convergence for the maximum partial sums of m-widely orthant dependent(m-WOD)random variables sequences under some general conditions.The results extend the complete convergence for m-WOD random variables to a much more general type complete convergence.As the sequences of m-WOD random variables represent a very broad class of dependent sequences,the results improve and generalize the corresponding ones in the literature.展开更多
In this paper,we give the double inequalities of a special quasi-arithmetic mean E(a,b)and the Seifert-like elliptic integral mean V(a,b)under the combination of generalized Heronian mean Hw(a,b),harmonic mean H(a,b)a...In this paper,we give the double inequalities of a special quasi-arithmetic mean E(a,b)and the Seifert-like elliptic integral mean V(a,b)under the combination of generalized Heronian mean Hw(a,b),harmonic mean H(a,b)and arithmetic mean A(a,b).As applications,we obtain two new optimal bounds for the second kind of complete elliptic integral".Finally,numerical experiments are performed to compare these with some known bounds of",and the improved effect is verified.展开更多
BACKGROUND Sorafenib has been the conventional treatment for advanced hepatocellular carcinoma(HCC)since 2008.While radiological complete responses are extremely rare,improved supportive care and multidisciplinary app...BACKGROUND Sorafenib has been the conventional treatment for advanced hepatocellular carcinoma(HCC)since 2008.While radiological complete responses are extremely rare,improved supportive care and multidisciplinary approaches in clinical practice may explain the recent increase in case reports and retrospective series documenting such responses.CASE SUMMARY This case series describes 3 patients with advanced HCC who achieved durable complete responses using first-line sorafenib therapy,even in the presence of portal vein thrombosis or extrahepatic spread,and highlights the potential for sustained remission in selected patients.Dermatologic toxicity and non-viral etiology may correlate with favorable outcomes;however,reliable predictive biomarkers for sorafenib response are lacking.CONCLUSION Future research into the etiology and molecular differences in HCC is necessary to develop more personalized therapy options.展开更多
Convolutional neural networks(CNNs)have shown remarkable success across numerous tasks such as image classification,yet the theoretical understanding of their convergence remains underdeveloped compared to their empir...Convolutional neural networks(CNNs)have shown remarkable success across numerous tasks such as image classification,yet the theoretical understanding of their convergence remains underdeveloped compared to their empirical achievements.In this paper,the first filter learning framework with convergence-guaranteed learning laws for end-to-end learning of deep CNNs is proposed.Novel update laws with convergence analysis are formulated based on the mathematical representation of each layer in convolutional neural networks.The proposed learning laws enable concurrent updates of weights across all layers of the deep convolutional neural network and the analysis shows that the training errors converge to certain bounds which are dependent on the approximation errors.Case studies are conducted on benchmark datasets and the results show that the proposed concurrent filter learning framework guarantees the convergence and offers more consistent and reliable results during training with a trade-off in performance compared to stochastic gradient descent methods.This framework represents a significant step towards enhancing the reliability and effectiveness of deep convolutional neural network by developing a theoretical analysis which allows practical implementation of the learning laws with automatic tuning of the learning rate to guarantee the convergence during training.展开更多
Unequal virtual water transfer may aggravate local water scarcity risk.However,the quantitative confirmation of a clear geographic convergence between virtual water transfer and water scarcity risk remains undetermine...Unequal virtual water transfer may aggravate local water scarcity risk.However,the quantitative confirmation of a clear geographic convergence between virtual water transfer and water scarcity risk remains undetermined.We present an analytical framework that reveals the spatial matching between global water scarcity risk and virtual water trade inequality.This framework integrates a three-dimensional water scarcity risk assessment,hybrid input-output analysis,pollution trade term construction,and geographic convergence identification.The framework is applied to 123 countries for long-term validation from 1991 to 2021.We show that despite global improvements in water efficiency and security,countries exceeding the maximum water vulnerability threshold have increased by 50%.South Asia is the largest net exporter of virtual water.Central Asia exhibits the most pronounced virtual water trade inequality.To achieve the same economic growth,Central Asia needs to pay several times the local water consumption costs of developed regions(15.9−83.6 times,2021).In the past 30 years,the average geographic convergence index exceeded 0.8.Countries facing severe water scarcity also exhibit pronounced inequalities in virtual water trade,indicating that a significant geographic convergence relationship exists.Effectively responding to this unsustainable relationship necessitates balancing both domestic resource risk management and global virtual water trade regulation.展开更多
Nereididae is a prolific annelid family widely distributed in the world oceans,especially in the Indo-Pacific Convergence Zone(IPCZ).However,its biogeographic pattern remains unexplored in IPCZ.To contribute to the un...Nereididae is a prolific annelid family widely distributed in the world oceans,especially in the Indo-Pacific Convergence Zone(IPCZ).However,its biogeographic pattern remains unexplored in IPCZ.To contribute to the understanding of biodiversity and biogeography of Nereididae in the IPCZ,we integrated historical data of species distributions with those of model-predicted ones to determine the biogeographic patterns of nereid species,from which we projected to its future distribution patterns for 2090-2100 under different climate scenarios(SSP1-1.9 and SSP5-8.5).Functional diversity within IPCZ was assessed using functional richness,functional evenness,and functional disparity.Divergence times within Nereididae were estimated using three DNA marker genes(COI,16S,and 18S rRNA),and a time tree was constructed based on a strict molecular clock model.The IPCZ was established as a key Nereididae biodiversity hotspot through distribution modelling of 256 species(44 genera),and temperature emerging as the predominant climatic driver of species distribution patterns.The distribution of species and functional diversity is notable for its non-centralized pattern.We projected that by the end of the century,areas of medium-to-high species richness will expand significantly under the low-emission SSP1-1.9 climate scenario.However,under the high-emission SSP5-8.5 scenario,the suitability of these regions significantly declines,posing an increasingly severe threat to biodiversity.In addition,by molecular clock analysis,we revealed that the evolutionary divergence of extant nereidid species occurred mainly in the Cretaceous and Jurassic,suggesting that paleogeographical and environmental events,such as oceanic anoxic events,might have played a pivotal role in shaping the evolutionary trajectory and ecological adaptations of marine annelids.These findings highlight the importance of considering both current biodiversity patterns and historical contexts in conservation planning,and provided insights into the potential factors on the biogeographic distribution and evolutionary processes of Nereididae.展开更多
In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which ...In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.展开更多
When patients initially present with atrial fibrillation along with an enlarged heart and heart failure, followed by atrioventricular block, it's essential to consider genetic factors.^([1])Genetic testing can off...When patients initially present with atrial fibrillation along with an enlarged heart and heart failure, followed by atrioventricular block, it's essential to consider genetic factors.^([1])Genetic testing can offer crucial diagnostic evidence, aiding in prognosis assessment and the adoption of appropriate treatment strategies.展开更多
In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the ran...In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.展开更多
This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence ...This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.展开更多
We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnum...We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.展开更多
In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some gen...In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.展开更多
In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing th...In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.展开更多
In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random variables.The results in this article improve and extend the results of the moving av...In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random variables.The results in this article improve and extend the results of the moving average process.mWOD random variables include WOD,m-NA,m-NOD and mEND random variables,so the results in the paper also promote the corresponding ones in WOD,m-NA,m-NOD,m-END random variables.展开更多
In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distri...In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.展开更多
In this paper, we investigate the complete convergence of double-indexed random- ly weighted sums of negatively orthant dependent （NOD） random variables. Some complete moment convergence and complete convergence of ...In this paper, we investigate the complete convergence of double-indexed random- ly weighted sums of negatively orthant dependent （NOD） random variables. Some complete moment convergence and complete convergence of this dependent sequence are presented, Marcinkiewicz-Zygmund-type strong law of large numbers is also obtained. Our results ex- tend some corresponding ones. In addition, some simulations are illustrated to show the convergence.展开更多
In this paper, the authors present some new results on complete moment convergence for arrays of rowwise negatively associated random variables. These results improve some previous known theorems.
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Re-accompanying Funding Project of Academic Achievements of Jingdezhen Ceramic University(Grant Nos.215/20506277,215/20506341)。
文摘The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.
基金supported by the National Social Science Fundation(Grant No.21BTJ040)the Project of Outstanding Young People in University of Anhui Province(Grant Nos.2023AH020037,SLXY2024A001).
文摘In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.
基金Supported by the Academic Achievement Re-cultivation Projects of Jingdezhen Ceramic University(Grant Nos.215/20506341215/20506277)the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)。
文摘Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.
基金Supported by the Academic Funding Projects for Top Talents in Universities of Anhui Province(gxbjZD2022067)Talent Planning Project of Tongling University(2022tlxyrc32)the Key Grant Project for Academic Leaders of Tongling University(2020tlxyxs31)。
文摘In this paper,the author obtains complete convergence for the maximum partial sums of m-widely orthant dependent(m-WOD)random variables sequences under some general conditions.The results extend the complete convergence for m-WOD random variables to a much more general type complete convergence.As the sequences of m-WOD random variables represent a very broad class of dependent sequences,the results improve and generalize the corresponding ones in the literature.
文摘In this paper,we give the double inequalities of a special quasi-arithmetic mean E(a,b)and the Seifert-like elliptic integral mean V(a,b)under the combination of generalized Heronian mean Hw(a,b),harmonic mean H(a,b)and arithmetic mean A(a,b).As applications,we obtain two new optimal bounds for the second kind of complete elliptic integral".Finally,numerical experiments are performed to compare these with some known bounds of",and the improved effect is verified.
文摘BACKGROUND Sorafenib has been the conventional treatment for advanced hepatocellular carcinoma(HCC)since 2008.While radiological complete responses are extremely rare,improved supportive care and multidisciplinary approaches in clinical practice may explain the recent increase in case reports and retrospective series documenting such responses.CASE SUMMARY This case series describes 3 patients with advanced HCC who achieved durable complete responses using first-line sorafenib therapy,even in the presence of portal vein thrombosis or extrahepatic spread,and highlights the potential for sustained remission in selected patients.Dermatologic toxicity and non-viral etiology may correlate with favorable outcomes;however,reliable predictive biomarkers for sorafenib response are lacking.CONCLUSION Future research into the etiology and molecular differences in HCC is necessary to develop more personalized therapy options.
基金supported by the Ministry of Education(MOE)Singapore,Academic Research Fund(AcRF)Tier 1(RG65/22)。
文摘Convolutional neural networks(CNNs)have shown remarkable success across numerous tasks such as image classification,yet the theoretical understanding of their convergence remains underdeveloped compared to their empirical achievements.In this paper,the first filter learning framework with convergence-guaranteed learning laws for end-to-end learning of deep CNNs is proposed.Novel update laws with convergence analysis are formulated based on the mathematical representation of each layer in convolutional neural networks.The proposed learning laws enable concurrent updates of weights across all layers of the deep convolutional neural network and the analysis shows that the training errors converge to certain bounds which are dependent on the approximation errors.Case studies are conducted on benchmark datasets and the results show that the proposed concurrent filter learning framework guarantees the convergence and offers more consistent and reliable results during training with a trade-off in performance compared to stochastic gradient descent methods.This framework represents a significant step towards enhancing the reliability and effectiveness of deep convolutional neural network by developing a theoretical analysis which allows practical implementation of the learning laws with automatic tuning of the learning rate to guarantee the convergence during training.
基金supported by National Natural Science Foundation of China(Grant No.52279027)National Key R&D Program of China(Grant No.2021YFC3200201)+1 种基金Key Research Project on Decision Consultation of the Strategic Development Department of China Association for Science and Technology(Grant No.2023070615CG111504)China Engineering Science and Technology Development Strategy Henan Research Institute Strategic Consulting Research Project(Grant No.2024HENYB01).
文摘Unequal virtual water transfer may aggravate local water scarcity risk.However,the quantitative confirmation of a clear geographic convergence between virtual water transfer and water scarcity risk remains undetermined.We present an analytical framework that reveals the spatial matching between global water scarcity risk and virtual water trade inequality.This framework integrates a three-dimensional water scarcity risk assessment,hybrid input-output analysis,pollution trade term construction,and geographic convergence identification.The framework is applied to 123 countries for long-term validation from 1991 to 2021.We show that despite global improvements in water efficiency and security,countries exceeding the maximum water vulnerability threshold have increased by 50%.South Asia is the largest net exporter of virtual water.Central Asia exhibits the most pronounced virtual water trade inequality.To achieve the same economic growth,Central Asia needs to pay several times the local water consumption costs of developed regions(15.9−83.6 times,2021).In the past 30 years,the average geographic convergence index exceeded 0.8.Countries facing severe water scarcity also exhibit pronounced inequalities in virtual water trade,indicating that a significant geographic convergence relationship exists.Effectively responding to this unsustainable relationship necessitates balancing both domestic resource risk management and global virtual water trade regulation.
基金Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB42000000)the National Natural Science Foundation of China(No.42376092)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(No.2022QNLM030004)。
文摘Nereididae is a prolific annelid family widely distributed in the world oceans,especially in the Indo-Pacific Convergence Zone(IPCZ).However,its biogeographic pattern remains unexplored in IPCZ.To contribute to the understanding of biodiversity and biogeography of Nereididae in the IPCZ,we integrated historical data of species distributions with those of model-predicted ones to determine the biogeographic patterns of nereid species,from which we projected to its future distribution patterns for 2090-2100 under different climate scenarios(SSP1-1.9 and SSP5-8.5).Functional diversity within IPCZ was assessed using functional richness,functional evenness,and functional disparity.Divergence times within Nereididae were estimated using three DNA marker genes(COI,16S,and 18S rRNA),and a time tree was constructed based on a strict molecular clock model.The IPCZ was established as a key Nereididae biodiversity hotspot through distribution modelling of 256 species(44 genera),and temperature emerging as the predominant climatic driver of species distribution patterns.The distribution of species and functional diversity is notable for its non-centralized pattern.We projected that by the end of the century,areas of medium-to-high species richness will expand significantly under the low-emission SSP1-1.9 climate scenario.However,under the high-emission SSP5-8.5 scenario,the suitability of these regions significantly declines,posing an increasingly severe threat to biodiversity.In addition,by molecular clock analysis,we revealed that the evolutionary divergence of extant nereidid species occurred mainly in the Cretaceous and Jurassic,suggesting that paleogeographical and environmental events,such as oceanic anoxic events,might have played a pivotal role in shaping the evolutionary trajectory and ecological adaptations of marine annelids.These findings highlight the importance of considering both current biodiversity patterns and historical contexts in conservation planning,and provided insights into the potential factors on the biogeographic distribution and evolutionary processes of Nereididae.
基金supported by the Project for Outstanding Young Talents in Bagui of Guangxi,the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NSFC(12371312)+2 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the Postdoctoral Fellowship Program of CPSF(GZC20241534)the Startup Project of Postdoctoral Scientific Research of Zhejiang Normal University(ZC304023924).
文摘In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.
基金Military Healthcare Special Scientific Research Project(25BJZ31, awarded to SHI XM)。
文摘When patients initially present with atrial fibrillation along with an enlarged heart and heart failure, followed by atrioventricular block, it's essential to consider genetic factors.^([1])Genetic testing can offer crucial diagnostic evidence, aiding in prognosis assessment and the adoption of appropriate treatment strategies.
基金supported by a grant from Ferdowsi University of Mashhad(NO.2/42843)
文摘In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.
基金Supported by the National Natural Science Foundation of China（11061012） Supported by the Natural Science Foundation of Guangxi（2010GXNSFA013121）
文摘This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.
基金Supported by the National Natural Science Foundation of China(11501004,11501005,11526033,11671012)the Natural Science Foundation of Anhui Province(1508085J06,1608085QA02)+1 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)
文摘In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.
基金supported by the National Science Foundation of China(11271161)
文摘In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.
基金Supported by the Academic Funding Projects for Top Talents in Universities of Anhui Province(gxbj ZD2022067,gxbj ZD2021078)the Philosophy and Social Sciences Planning Project of Anhui Province(AHSKY2018D98)。
文摘In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random variables.The results in this article improve and extend the results of the moving average process.mWOD random variables include WOD,m-NA,m-NOD and mEND random variables,so the results in the paper also promote the corresponding ones in WOD,m-NA,m-NOD,m-END random variables.
基金National Natural Science Foundation of China (Grant Nos.12061028, 71871046)Support Program of the Guangxi China Science Foundation (Grant No.2018GXNSFAA281011)。
文摘In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1150100511671012+8 种基金11701004)the Natural Science Foundation of Anhui Province(Grant Nos.1508085J061608085QA02)Science Research Project of Anhui Colleges(Grant Nos.KJ2015A065KJ2016A027KJ2017A027)Quality Engineering Project of Anhui Province(Grant Nos.2015jyxm054ZLTS2015053)Students Innovation Training Program of Anhui University(Grant No.201610357002)
文摘In this paper, we investigate the complete convergence of double-indexed random- ly weighted sums of negatively orthant dependent （NOD） random variables. Some complete moment convergence and complete convergence of this dependent sequence are presented, Marcinkiewicz-Zygmund-type strong law of large numbers is also obtained. Our results ex- tend some corresponding ones. In addition, some simulations are illustrated to show the convergence.
基金Foundation item： Supported by the Humanities and Social Sciences Foundation for the Youth Schol- ars of Ministry of Education of China（12YJCZH217） Supported by the National Natural Science Foun- dation of China（l1271020）+1 种基金 Supported by the Key Natural Science Foundation of Anhui Educational Committee（KJ2011A139） Supported by the Natural Science Foundation of Anhui Province（1308085MA03, 1208085MA 11）
文摘In this paper, the authors present some new results on complete moment convergence for arrays of rowwise negatively associated random variables. These results improve some previous known theorems.
