Pub Date : 2018-07-28DOI: 10.14708/MA.V35I49/08.1383
K. Skórnik, R. Rudnicki
{"title":"Professor Andrzej Lasota (1932-2006)","authors":"K. Skórnik, R. Rudnicki","doi":"10.14708/MA.V35I49/08.1383","DOIUrl":"https://doi.org/10.14708/MA.V35I49/08.1383","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44720399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/MA.V35I49/08.1390
Anita Małoń, Dagmara Ziółkowska
Adapting the classical Pearson’s chi-square goodness-of-fit test for testing composite hypotheses brings serious problems with estimation of unknown parameters. An interesting solution which eliminates them was proposed by Dzhaparidze and Nikulin. The most important advantage of their solution is a possibility of using arbitrary estimators satisfying only a natural and weak condition. The aim of the present article is to popularize this solution. We provide a complete, short and, what is more elementary proof of the main theorem on asymptotic distribution of the test statistic. In addition, we prove that the constructed test belongs to a general class of score tests what advocates for its good properties. Finally, as an example, we give a typical implementation of the test to testing in location and scale family.
{"title":"Chi-square type goodness of fit tests for composite hypothesis","authors":"Anita Małoń, Dagmara Ziółkowska","doi":"10.14708/MA.V35I49/08.1390","DOIUrl":"https://doi.org/10.14708/MA.V35I49/08.1390","url":null,"abstract":"Adapting the classical Pearson’s chi-square goodness-of-fit test for testing composite hypotheses brings serious problems with estimation of unknown parameters. An interesting solution which eliminates them was proposed by Dzhaparidze and Nikulin. The most important advantage of their solution is a possibility of using arbitrary estimators satisfying only a natural and weak condition. The aim of the present article is to popularize this solution. We provide a complete, short and, what is more elementary proof of the main theorem on asymptotic distribution of the test statistic. In addition, we prove that the constructed test belongs to a general class of score tests what advocates for its good properties. Finally, as an example, we give a typical implementation of the test to testing in location and scale family.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46479078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/MA.V35I49/08.1384
M. Mackey
This is an account of my scientific and personal friendship with Prof. Andrzej(Andy) Aleksander Lasota from 1977 until his death 28 December, 2006. It is a tale that fascinates me because of the intertwined links between many people both East and West of several generations, and it illustrates what I feel is the strength and beauty of the personal side of the scientific endeavor.
这是我与Andrzej(Andy) Aleksander Lasota教授自1977年至2006年12月28日去世的科学和个人友谊的记述。这是一个让我着迷的故事，因为东方人和西方人几代人之间的联系交织在一起，它说明了我所感受到的科学努力的个人方面的力量和美丽。
{"title":"Adventures in Poland: Having Fun and Doing Research with Andrzej Lasota","authors":"M. Mackey","doi":"10.14708/MA.V35I49/08.1384","DOIUrl":"https://doi.org/10.14708/MA.V35I49/08.1384","url":null,"abstract":"This is an account of my scientific and personal friendship with Prof. Andrzej(Andy) Aleksander Lasota from 1977 until his death 28 December, 2006. It is a tale that fascinates me because of the intertwined links between many people both East and West of several generations, and it illustrates what I feel is the strength and beauty of the personal side of the scientific endeavor.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44000416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/MA.V35I49/08.1388
T. Ledwina
We present and discuss the notion of asymptotic efficiency of estimators as introduced by Hajek and Le Cam. We give also some general construction of a class of asymptotically efficient estimators of Euclidean parameters. Moreover, we briefly indicate some generalizations of the discussed ideas to the case of semiparametric models. We show also that technical results obtained in the asymptotic theory of efficient estimation can be successfully used in asymptotic theory of testing. The selection of the material is highly subjective and to a little extent reflects complexity of several problems and range of results available in present-day literature. The paper is a shortened version of invited series of lectures presented at the Conference on Mathematical Statistics WISŁA 2005. Its main purpose is to show that classic approach to define efficiency was not satisfactory and to discuss how, for some class of problems, this question was solved in a natural and elegant way.
{"title":"On the asymptotic efficiency of estimators","authors":"T. Ledwina","doi":"10.14708/MA.V35I49/08.1388","DOIUrl":"https://doi.org/10.14708/MA.V35I49/08.1388","url":null,"abstract":"We present and discuss the notion of asymptotic efficiency of estimators as introduced by Hajek and Le Cam. We give also some general construction of a class of asymptotically efficient estimators of Euclidean parameters. Moreover, we briefly indicate some generalizations of the discussed ideas to the case of semiparametric models. We show also that technical results obtained in the asymptotic theory of efficient estimation can be successfully used in asymptotic theory of testing. The selection of the material is highly subjective and to a little extent reflects complexity of several problems and range of results available in present-day literature. The paper is a shortened version of invited series of lectures presented at the Conference on Mathematical Statistics WISŁA 2005. Its main purpose is to show that classic approach to define efficiency was not satisfactory and to discuss how, for some class of problems, this question was solved in a natural and elegant way.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48556642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/MA.V35I49/08.1389
Marcin Dudziński, K. Furmańczyk
In our paper, we consider different approaches to the problem of simultaneous testing of many null hypotheses. In this context, we discuss the single-step, the step-down and the step-up procedures of multiple testing. In particular, we are concerned with their properties and applications in the control of the error rates, such as:FW ER, k-FWER, FDP, FDR, pFDR. The mentioned procedures are intensively used in the DNA microarrays analysis, which enables the monitoring of expression levels of many genes simultaneously and is widely applied in recent medical diagnostics, treatment and research.
在本文中，我们考虑了同时检验多个零假设问题的不同方法。在此背景下，我们讨论了多重测试的单步、降压和升压过程。特别地，我们关注它们的性质及其在错误率控制中的应用，如:FW ER, k-FWER, FDP, FDR, pFDR。上述程序在DNA微阵列分析中被广泛使用，可以同时监测许多基因的表达水平，并广泛应用于最近的医学诊断、治疗和研究。
{"title":"Simultaneous testing procedures of many null hypotheses and their applications in the DNA microarrays analysis","authors":"Marcin Dudziński, K. Furmańczyk","doi":"10.14708/MA.V35I49/08.1389","DOIUrl":"https://doi.org/10.14708/MA.V35I49/08.1389","url":null,"abstract":"In our paper, we consider different approaches to the problem of simultaneous testing of many null hypotheses. In this context, we discuss the single-step, the step-down and the step-up procedures of multiple testing. In particular, we are concerned with their properties and applications in the control of the error rates, such as:FW ER, k-FWER, FDP, FDR, pFDR. The mentioned procedures are intensively used in the DNA microarrays analysis, which enables the monitoring of expression levels of many genes simultaneously and is widely applied in recent medical diagnostics, treatment and research.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41610706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/ma.v35i49/08.1386
A. Dawidowicz
{"title":"On the Avez method and its generalizations","authors":"A. Dawidowicz","doi":"10.14708/ma.v35i49/08.1386","DOIUrl":"https://doi.org/10.14708/ma.v35i49/08.1386","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46615575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/MA.V35I49/08.1391
J. Jarosz-Nowak
In medical studies quality of assessment is of great importance. Typically it is characterized by reliability. A fundamental sense of interobserver reliability is to evaluate a degree of agreement between independent judges examining the same objects. The paper is an evaluation of some interrater reliability measures and their interpretation. Cohen’s kappa and Scott’s coefficient are considered. We describe models and connections between coefficients defined for dichotomous and politomous data. We show that abovementioned estimators of kappa for classification into more than 2 categories are weighted averages of kappas in binary models defined for each category separately.
{"title":"Models of assessing the extent of agreement beteween raters using kappa coefficients","authors":"J. Jarosz-Nowak","doi":"10.14708/MA.V35I49/08.1391","DOIUrl":"https://doi.org/10.14708/MA.V35I49/08.1391","url":null,"abstract":"In medical studies quality of assessment is of great importance. Typically it is characterized by reliability. A fundamental sense of interobserver reliability is to evaluate a degree of agreement between independent judges examining the same objects. The paper is an evaluation of some interrater reliability measures and their interpretation. Cohen’s kappa and Scott’s coefficient are considered. We describe models and connections between coefficients defined for dichotomous and politomous data. We show that abovementioned estimators of kappa for classification into more than 2 categories are weighted averages of kappas in binary models defined for each category separately.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43740072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/ma.v35i49/08.1393
W. Kosinski
{"title":"Erratum to the article I. Czochralski, MatStos 7, 2006","authors":"W. Kosinski","doi":"10.14708/ma.v35i49/08.1393","DOIUrl":"https://doi.org/10.14708/ma.v35i49/08.1393","url":null,"abstract":"","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42038123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-28DOI: 10.14708/MA.V35I49/08.1385
J. Socala, W. Kosinski
Markovian operators, non-negative linear operators and its subgroups play a significant role for the description of phenomena observed in the nature. Research on asymptotic stability is one of the main issues in this respect. A. Lasota and J. A. Yorke proved in 1982 that the necessary and sufficient condition of the asymptotic stability of a Markovian operator is the existence of a non-trivial lower-bound function. In the present paper it is shown how the method of lower-bound function can be applied to the investigation of genetic algorithms. Genetic algorithms considered used for solving of non-smooth optimization problems are compositions of two random operators: selection and mutation. The compositions are Markovian matrices.
{"title":"Application of the lower-bound function method to the investigation of the convergence of genetic algorithms","authors":"J. Socala, W. Kosinski","doi":"10.14708/MA.V35I49/08.1385","DOIUrl":"https://doi.org/10.14708/MA.V35I49/08.1385","url":null,"abstract":"Markovian operators, non-negative linear operators and its subgroups play a significant role for the description of phenomena observed in the nature. Research on asymptotic stability is one of the main issues in this respect. A. Lasota and J. A. Yorke proved in 1982 that the necessary and sufficient condition of the asymptotic stability of a Markovian operator is the existence of a non-trivial lower-bound function. In the present paper it is shown how the method of lower-bound function can be applied to the investigation of genetic algorithms. Genetic algorithms considered used for solving of non-smooth optimization problems are compositions of two random operators: selection and mutation. The compositions are Markovian matrices.","PeriodicalId":36622,"journal":{"name":"Mathematica Applicanda","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41348866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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