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Entropic upper bound for Bayes risk in the quantum case 量子情形下Bayes风险的熵上界
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.9
Rafał M. Wieczorek, H. Podsędkowska
{"title":"Entropic upper bound for Bayes risk in the quantum case","authors":"Rafał M. Wieczorek, H. Podsędkowska","doi":"10.19195/0208-4147.38.2.9","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.9","url":null,"abstract":"The entropic upper bound for Bayes risk in a general quantum case is presented. We obtained generalization of the entropic lower bound for probability of detection. Our result indicates upper bound for Bayes risk in a particular case of loss function – for probability of detection in a pretty general setting of an arbitrary finite von Neumann algebra. It is also shown under which condition the indicated upper bound is achieved.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48461076","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
An equivalent characterization of weak BMO martingale spaces 弱BMO鞅空间的一个等价刻画
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.3
Dejian Zhou, Weiwei Li, Y. Jiao
{"title":"An equivalent characterization of weak BMO martingale spaces","authors":"Dejian Zhou, Weiwei Li, Y. Jiao","doi":"10.19195/0208-4147.38.2.3","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.3","url":null,"abstract":"In this paper, we give an equivalent characterization of weak BMO martingale spaces due to Ferenc Weisz 1998.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48363675","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 longest runs in Markov chains 在马尔可夫链的最长运行中
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.8
Zhenxia Liu, Xiangfeng Yang
{"title":"On the longest runs in Markov chains","authors":"Zhenxia Liu, Xiangfeng Yang","doi":"10.19195/0208-4147.38.2.8","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.8","url":null,"abstract":"In the first n steps of a two-state success and failure Markov chain, the longest success run Ln has been attracting considerable attention due to its various applications. In this paper, we study Ln in terms of its two closely connected properties: moment generating function and large deviations. This study generalizes several existing results in the literature, and also finds an application in statistical inference. Our method on the moment generating function is based on a global estimate of the cumulative distribution function of Ln proposed in this paper, and the proofs of the large deviations include the Gärtner–Ellis theorem and the moment generating function.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42368931","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: 4
Supermodular ordering of Poisson and binomial random vectors by tree-based correlations 基于树相关的泊松和二项随机向量的超模排序
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.7
Bünyamin Kızıldemir, Nicolas Privault
{"title":"Supermodular ordering of Poisson and binomial random vectors by tree-based correlations","authors":"Bünyamin Kızıldemir, Nicolas Privault","doi":"10.19195/0208-4147.38.2.7","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.7","url":null,"abstract":"We construct a dependence structure for binomial, Poisson and Gaussian random vectors, based on partially ordered binary trees and sums of independent random variables. Using this construction, we characterize the supermodular ordering of such random vectors via the componentwise ordering of their covariance matrices. For this, we apply Möbius inversion techniques on partially ordered trees, which allow us to connect the Lévy measures of Poisson random vectors on the discrete d-dimensional hypercube to their covariance matrices.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45368088","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: 2
Preservation properties of stochastic orders by transformation to Harris family Harris族变换下随机阶的保存性质
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.10
S. Abbasi, M. H. Alamatsaz
{"title":"Preservation properties of stochastic orders by transformation to Harris family","authors":"S. Abbasi, M. H. Alamatsaz","doi":"10.19195/0208-4147.38.2.10","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.10","url":null,"abstract":"Stochastic comparisons of lifetime characteristics of reliability systems and their components are of common use in lifetime analysis. In this paper, using Harris family distributions, we compare lifetimes of two series systems with random number of components, with respect to several types of stochastic orders. Our results happen to enfold several previous findings in this connection. We shall also show that several stochastic orders and ageing characteristics, such as IHRA, DHRA, NBU, and NWU, are inherited by transformation to Harris family. Finally, some refinements are made concerning related existing results in the literature.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43021728","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: 2
Prediction intervals and regions for multivariate time series models with sieve bootstrap 筛子自举多变量时间序列模型的预测区间和区域
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.5
Maciej Kawecki, R. Różański, Grzegorz Chłapiński, M. Hławka, Krzysztof Jamróz, A. Zagdanski
{"title":"Prediction intervals and regions for multivariate time series models with sieve bootstrap","authors":"Maciej Kawecki, R. Różański, Grzegorz Chłapiński, M. Hławka, Krzysztof Jamróz, A. Zagdanski","doi":"10.19195/0208-4147.38.2.5","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.5","url":null,"abstract":"In the paper, the construction of unconditional bootstrap prediction intervals and regions for some class of second order stationary multivariate linear time series models is considered. Our approach uses the sieve bootstrap procedure introduced by Kreiss 1992 and Bühlmann 1997. Basic theoretical results concerning consistency of the bootstrap replications and the bootstrap prediction regions are proved. We present a simulation study comparing the proposed bootstrap methods with the Box–Jenkins approach.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47671696","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
Boundary value problems for the Dunkl Laplacian Dunkl-Laplacian算子的边值问题
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.1
M. Ben Chrouda, Khalifa El Mabrouk, Kods Hassine
{"title":"Boundary value problems for the Dunkl Laplacian","authors":"M. Ben Chrouda, Khalifa El Mabrouk, Kods Hassine","doi":"10.19195/0208-4147.38.2.1","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.1","url":null,"abstract":"Let Δk be the Dunkl Laplacian on ℜd associated with a reflection group W and a multiplicity function k. The purpose of this paper is to establish the existence and the uniqueness of a positive solution on the unit ball B of ℜd to the following boundary value problem:Δku = φu in B and u = ƒ on ∂BWe distinguish two cases of nonnegative perturbation φ: trivial and nontrivial.   ","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49261267","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 strongly orthogonal martingales in UMD Banach spaces UMD-Banach空间中的强正交鞅
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-19 DOI: 10.37190/0208-4147.41.1.10
I. Yaroslavtsev
{"title":"On strongly orthogonal martingales in UMD Banach spaces","authors":"I. Yaroslavtsev","doi":"10.37190/0208-4147.41.1.10","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.10","url":null,"abstract":"In the present paper we introduce the notion of strongly orthogonal martingales. Moreover, we show that for any UMD Banach space $X$ and for any $X$-valued strongly orthogonal martingales $M$ and $N$ such that $N$ is weakly differentially subordinate to $M$ one has that for any $1<p<infty$ [ mathbb E |N_t|^p leq chi_{p, X}^p mathbb E |M_t|^p,;;; tgeq 0, ] with the sharp constant $chi_{p, X}$ being the norm of a decoupling-type martingale transform and being within the range [ maxBigl{sqrt{beta_{p, X}}, sqrt{hbar_{p,X}}Bigr} leq max{beta_{p, X}^{gamma,+}, beta_{p, X}^{gamma, -}} leq chi_{p, X} leq min{beta_{p, X}, hbar_{p,X}}, ] where $beta_{p, X}$ is the UMD$_p$ constant of $X$, $hbar_{p, X}$ is the norm of the Hilbert transform on $L^p(mathbb R; X)$, and $beta_{p, X}^{gamma,+}$ and $ beta_{p, X}^{gamma, -}$ are the Gaussian decoupling constants.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43043742","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
M-estimation of the mixed-type generalized linear model 混合型广义线性模型的m估计
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.11
Ying Dong, Lixin Song, Mingqiu Wang, Muhammad Amin
{"title":"M-estimation of the mixed-type generalized linear model","authors":"Ying Dong, Lixin Song, Mingqiu Wang, Muhammad Amin","doi":"10.19195/0208-4147.38.1.11","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.11","url":null,"abstract":"To investigate the features of the individual from the mixedtype model, a novel model, named the mixed-type generalized linear model, is proposed firstly in this work, which is verified to be realistic and useful. We consider the robustness of M-estimation to estimate the unknown parameters of the mixed-type generalized linear model. By applying the law of large numbers and the central limit theorem, the consistency and asymptotic normality of the M-estimation for the mixed-type generalized linear model are proved with regularity assumptions. At last, in order to evaluate the finite sample performance of the estimator for the new model, several applied instances are presented, which show the good performance of the estimator.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44144023","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 exact strong laws of large numbers under general dependence conditions 关于一般依赖条件下的精确强大数定律
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.6
A. Adler, P. Matuła
{"title":"On exact strong laws of large numbers under general dependence conditions","authors":"A. Adler, P. Matuła","doi":"10.19195/0208-4147.38.1.6","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.6","url":null,"abstract":"We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49506051","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: 14
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