Pub Date : 2020-01-01DOI: 10.37190/0208-4147.41.2.5
Un Cig Ji, Peng Cheng Ma
{"title":"Wick calculus for vector-valued Gaussian white noise unctionals","authors":"Un Cig Ji, Peng Cheng Ma","doi":"10.37190/0208-4147.41.2.5","DOIUrl":"https://doi.org/10.37190/0208-4147.41.2.5","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997176","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}
Pub Date : 2020-01-01DOI: 10.37190/0208-4147.41.1.5
A. Pakes
This paper obtains a necessary and sufficient condition for a weak law of large numbers for weighted averages of positive-valued independent random variables whose distributions belong to a class which includes the F-scheme of record theory. Additional general conditions are found under which the weak law extends to a strong law with the same norming. Examples show these conditions can be fulfilled, and that if they are not, then the weighted averages exhibit multiple growth rates. 2020 Mathematics Subject Classification: Primary 60F05, 60F15; Secondary 60E10.
{"title":"Weighted Laws of Large Numbers for a class of independent summands","authors":"A. Pakes","doi":"10.37190/0208-4147.41.1.5","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.5","url":null,"abstract":"This paper obtains a necessary and sufficient condition for a weak law of large numbers for weighted averages of positive-valued independent random variables whose distributions belong to a class which includes the F-scheme of record theory. Additional general conditions are found under which the weak law extends to a strong law with the same norming. Examples show these conditions can be fulfilled, and that if they are not, then the weighted averages exhibit multiple growth rates. 2020 Mathematics Subject Classification: Primary 60F05, 60F15; Secondary 60E10.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996991","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}
Pub Date : 2020-01-01DOI: 10.37190/0208-4147.41.1.6
T. Bednarski, P. Nowak
It is argued that inference based on the Cox regression model and the partial likelihood estimator is possible for various extensions of the model, which in particular include an arbitrary frailty variable. We demonstrate that the estimator in such a general setup is Fisher consistent up to a scaling factor under symmetry type distributional assumptions on explanatory variables. A simulation experiment shows exemplary behaviour of the estimator and also of a test of fit based on the Anderson–Darling statistic for different Cox model extensions. 2020 Mathematics Subject Classification: Primary 62N01; Secondary 62F12.
{"title":"Scaled Fisher consistency of partial likelihood estimator in the Cox model with arbitrary frailty","authors":"T. Bednarski, P. Nowak","doi":"10.37190/0208-4147.41.1.6","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.6","url":null,"abstract":"It is argued that inference based on the Cox regression model and the partial likelihood estimator is possible for various extensions of the model, which in particular include an arbitrary frailty variable. We demonstrate that the estimator in such a general setup is Fisher consistent up to a scaling factor under symmetry type distributional assumptions on explanatory variables. A simulation experiment shows exemplary behaviour of the estimator and also of a test of fit based on the Anderson–Darling statistic for different Cox model extensions. 2020 Mathematics Subject Classification: Primary 62N01; Secondary 62F12.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997003","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}
Pub Date : 2020-01-01DOI: 10.37190/0208-4147.41.1.2
M. Lifshits, A. Siuniaev
We consider the kinetic energy of the taut strings accompanying trajectories of a Wiener process and a random walk. Under certain assumptions on the band width, it is shown that the energy of a taut string accompanying a random walk within a band satisfies the same strong law of large numbers as proved earlier for a Wiener process and a fixed band width. New results for Wiener processes are also obtained. 2020 Mathematics Subject Classification: Primary 60G15; Secondary 60G17, 60F15.
{"title":"Energy of taut strings accompanying random walk","authors":"M. Lifshits, A. Siuniaev","doi":"10.37190/0208-4147.41.1.2","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.2","url":null,"abstract":"We consider the kinetic energy of the taut strings accompanying trajectories of a Wiener process and a random walk. Under certain assumptions on the band width, it is shown that the energy of a taut string accompanying a random walk within a band satisfies the same strong law of large numbers as proved earlier for a Wiener process and a fixed band width. New results for Wiener processes are also obtained. 2020 Mathematics Subject Classification: Primary 60G15; Secondary 60G17, 60F15.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996913","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}
Pub Date : 2020-01-01DOI: 10.37190/0208-4147.41.1.7
M. Brzozowski, A. Osȩkowski
{"title":"Weighted maximal inequalities for martingale transforms","authors":"M. Brzozowski, A. Osȩkowski","doi":"10.37190/0208-4147.41.1.7","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.7","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997013","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}
Pub Date : 2020-01-01DOI: 10.37190/0208-4147.41.1.11
L. Klotz, J. M. Medina
{"title":"JH-singularity and JH-regularity of multivariate stationary processes over LCA groups","authors":"L. Klotz, J. M. Medina","doi":"10.37190/0208-4147.41.1.11","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.11","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"168 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996902","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}
Pub Date : 2020-01-01DOI: 10.37190/0208-4147.41.1.8
G. Volovskiy, S. Bedbur, U. Kamps
Estimation of model parameters of sequential order statistics under linear and nonlinear link function assumptions is considered. Utilizing the arising curved exponential family structure, conditions for existence and uniqueness as well as the validity of asymptotic properties of maximum likelihood estimators are stated. Minimal sufficiency and completeness of the associated canonical statistics are discussed. 2020 Mathematics Subject Classification: Primary 62F10; Secondary 62N05, 62N02.
{"title":"Link functions for parameters of sequential order statistics and curved exponential families","authors":"G. Volovskiy, S. Bedbur, U. Kamps","doi":"10.37190/0208-4147.41.1.8","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.8","url":null,"abstract":"Estimation of model parameters of sequential order statistics under linear and nonlinear link function assumptions is considered. Utilizing the arising curved exponential family structure, conditions for existence and uniqueness as well as the validity of asymptotic properties of maximum likelihood estimators are stated. Minimal sufficiency and completeness of the associated canonical statistics are discussed. 2020 Mathematics Subject Classification: Primary 62F10; Secondary 62N05, 62N02.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997059","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}
Pub Date : 2019-11-18DOI: 10.37190/0208-4147.41.2.3
M. Ledoux, Jie-Xiang Zhu
This article is a continuation of the papers [8,9] in which the optimal matching problem, and the related rates of convergence of empirical measures for Gaussian samples are addressed. A further step in both the dimensional and Kantorovich parameters is achieved here, proving that, given $X_1, ldots, X_n$ independent random variables with common distribution the standard Gaussian measure $mu$ on $mathbb{R}^d$, $d geq 3$, and $mu_n , = , frac 1n sum_{i=1}^n delta_{X_i}$ the associated empirical measure, $$ mathbb{E} big( mathrm {W}_p^p (mu_n , mu )big ) , approx , frac {1}{n^{p/d}} $$ for any $1leq p < d$, where $mathrm {W}_p$ is the $p$-th Kantorovich metric. The proof relies on the pde and mass transportation approach developed by L. Ambrosio, F. Stra and D. Trevisan in a compact setting.
{"title":"On optimal matching of Gaussian samples III","authors":"M. Ledoux, Jie-Xiang Zhu","doi":"10.37190/0208-4147.41.2.3","DOIUrl":"https://doi.org/10.37190/0208-4147.41.2.3","url":null,"abstract":"This article is a continuation of the papers [8,9] in which the optimal matching problem, and the related rates of convergence of empirical measures for Gaussian samples are addressed. A further step in both the dimensional and Kantorovich parameters is achieved here, proving that, given $X_1, ldots, X_n$ independent random variables with common distribution the standard Gaussian measure $mu$ on $mathbb{R}^d$, $d geq 3$, and $mu_n , = , frac 1n sum_{i=1}^n delta_{X_i}$ the associated empirical measure, $$ \u0000mathbb{E} big( mathrm {W}_p^p (mu_n , mu )big ) , approx , frac {1}{n^{p/d}} $$ for any $1leq p < d$, where $mathrm {W}_p$ is the $p$-th Kantorovich metric. The proof relies on the pde and mass transportation approach developed by L. Ambrosio, F. Stra and D. Trevisan in a compact setting.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997116","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}
Pub Date : 2019-06-10DOI: 10.19195/0208-4147.39.1.14
Kouji Yamamuro
Complex integrals associated with homogeneous independently scattered random measures on the line are discussed. Theorems corresponding to Cauchy’s theorem and the residue theorem are given. Furthermore, the converse of Cauchy’s theorem is discussed.
{"title":"Stochastic complex integrals associated with homogeneous independently scattered random measures on the line","authors":"Kouji Yamamuro","doi":"10.19195/0208-4147.39.1.14","DOIUrl":"https://doi.org/10.19195/0208-4147.39.1.14","url":null,"abstract":"Complex integrals associated with homogeneous independently scattered random measures on the line are discussed. Theorems corresponding to Cauchy’s theorem and the residue theorem are given. Furthermore, the converse of Cauchy’s theorem is discussed.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49436528","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}
Pub Date : 2019-06-10DOI: 10.19195/0208-4147.39.1.1
M. Mahdizadeh, Ehsan Zamanzade
Ranked set sampling RSS is a data collection method that allows us to direct attention toward measurements of more representative sample units. This article deals with estimating a time-dependent reliability measure under a generalization of the RSS. Some results concerning optimal properties of the proposed estimator are presented. Monte Carlo simulation is employed to assess performance of the estimator. A sport data set is finally analyzed.
{"title":"Dynamic reliability estimation in a rank-based design","authors":"M. Mahdizadeh, Ehsan Zamanzade","doi":"10.19195/0208-4147.39.1.1","DOIUrl":"https://doi.org/10.19195/0208-4147.39.1.1","url":null,"abstract":"Ranked set sampling RSS is a data collection method that allows us to direct attention toward measurements of more representative sample units. This article deals with estimating a time-dependent reliability measure under a generalization of the RSS. Some results concerning optimal properties of the proposed estimator are presented. Monte Carlo simulation is employed to assess performance of the estimator. A sport data set is finally analyzed.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47547779","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：