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On the Application of the Bootstrap: Coefficient of Variation, Contingency Table, Information Theory and Ranked Set Sampling
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Mathematical statistics)
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with the bootstrap method. Three decades after the seminal paper by Bradly Efron, still the horizons of this method need more exploration. The research presented herein has stepped into different fields of statistics where the bootstrap method can be utilized as a fundamental statistical tool in almost any application. The thesis considers various statistical problems, which is explained briefly below.

Bootstrap method: A comparison of the parametric and the nonparametric bootstrap of variance is presented. The bootstrap of ranked set sampling is dealt with, as well as the wealth of theories and applications on the RSS bootstrap that exist nowadays. Moreover, the performance of RSS in resampling is explored. Furthermore, the application of the bootstrap method in the inference of contingency table test is studied.

Coefficient of variation: This part shows the capacity of the bootstrap for inferring the coefficient of variation, a task which the asymptotic method does not perform very well.

Information theory: There are few works on the study of information theory, especially on the inference of entropy. The papers included in this thesis try to achieve the inference of entropy using the bootstrap method. 

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics , 2011. , 63 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 73
Keyword [en]
Bootstrap method; Categorical data; Coefficient of variation; Entropy; Exponential family; Monte Carlo investigation; Informational energy; Ranked set sampling; Variance-stabilization transformation
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:uu:diva-159206ISBN: 978-91-506-2237-9 (print)OAI: oai:DiVA.org:uu-159206DiVA: diva2:443740
Public defence
2011-11-11, Polhemsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 13:00 (English)
Opponent
Supervisors
Available from: 2011-10-28 Created: 2011-09-25 Last updated: 2011-10-28Bibliographically approved
List of papers
1. A comparison of bootstrap methods for variance estimation
Open this publication in new window or tab >>A comparison of bootstrap methods for variance estimation
2010 (English)In: Journal of Statistical Theory and ApplicationsArticle in journal (Refereed) Published
Abstract [en]

This paper presents a comparison of the nonparametric and parametric bootstrapmethods, when the statistic of interest is the sample variance estimator. Conditionswhen the nonparametric bootstrap method of variance performs better than the para-metric bootstrap method are described

Keyword
Bootstrap; Nonparametric; Parametric; Kurtosis; Variance.
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-158976 (URN)
Available from: 2011-09-19 Created: 2011-09-19
2. On the Resampling of the Unbalanced Ranked Set Sample
Open this publication in new window or tab >>On the Resampling of the Unbalanced Ranked Set Sample
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper considers the bootstrap approach of the unbalanced Ranked Set Sampling (RSS) method. Herethe sequence bootstrap is used to shift the analysis of the unbalanced RSS method to an analysis ofthe balanced RSS sample, and balanced RSS is also discussed. Here the consequences of differentalgorithms for carrying out resampling are discussed. The pro­posed methods are studied using Monte Carloinvestigations. Furthermore, the theoretical approach is discussed.

Keyword
Bootstrap method; Monte Carlo simulation; Ranked set sample
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-158983 (URN)
Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2012-02-16
3. On the efficiency of bootstrap method into the analysis contingency table
Open this publication in new window or tab >>On the efficiency of bootstrap method into the analysis contingency table
2011 (English)In: Computer Methods and Programs in Biomedicine, ISSN 0169-2607, E-ISSN 1872-7565, Vol. 104, no 2, 182-187 p.Article in journal (Refereed) Published
Abstract [en]

The bootstrap method is a computer intensive statistical method that is widely used in performing nonparametric inference. Categorica ldata analysis,inparticular the analysis of contingency tables, is commonly used in applied field. This work considers nonparametric bootstrap tests for the analysis of contingency tables. There are only a few research papers which exploit this field. The p-values of tests in contingency tables are discrete and should be uniformly distributed under the null hypothesis. The results of this article show that corresponding bootstrap versions work better than the standard tests. Properties of the proposed tests are illustrated and discussed using Monte Carlo simulations. This article concludes with an analytical example that examines the performance of the proposed tests and the confidence interval of the association coefficient.

Keyword
Association coefficient, Bootstrap method, Chi-squared test, Contingency table, Monte Carlo simulation
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-158978 (URN)10.1016/j.cmpb.2011.01.007 (DOI)000296945100018 ()
Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2017-12-08Bibliographically approved
4. An Improvement of the Nonparametric Bootstrap Test for the Comparison of the Coefficient of Variations
Open this publication in new window or tab >>An Improvement of the Nonparametric Bootstrap Test for the Comparison of the Coefficient of Variations
2010 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 39, no 9, 1726-1734 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we propose a new test for examining the equality of the coefficient of variation between two different populations. The proposed test is based on the nonparametric bootstrap method. It appears to yield several appreciable advantages over the current tests. The quick and easy implementation of the test can be considered as advantages of the proposed test. The test is examined by the Monte Carlo simulations, and also evaluated using various numerical studies.

Keyword
Bootstrap method, Coefficient of variation, Monte Carlo simulation
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-134888 (URN)10.1080/03610918.2010.512693 (DOI)000282124000004 ()
Available from: 2010-12-02 Created: 2010-12-02 Last updated: 2017-12-12Bibliographically approved
5. Assessing the coefficient of variations of chemical data using bootstrap method
Open this publication in new window or tab >>Assessing the coefficient of variations of chemical data using bootstrap method
2011 (English)In: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 25, no 6, 295-300 p.Article in journal (Refereed) Published
Abstract [en]

The coefficient of variation is frequently used in the comparison and precision of results with different scales. This work examines the comparison of the coefficient of variation without any assumptions about the underlying distribution. A family of tests based on the bootstrap method is proposed, and its properties are illustrated using Monte Carlo simulations. The proposed method is applied to chemical experiments with iid and non-iid observations.

Keyword
bootstrap method, coefficient of variation, Monte Carlo simulation
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-156490 (URN)10.1002/cem.1350 (DOI)000292542300002 ()
Available from: 2011-07-25 Created: 2011-07-25 Last updated: 2017-12-08Bibliographically approved
6. The Comparison of Entropies  using the Resampling Method
Open this publication in new window or tab >>The Comparison of Entropies  using the Resampling Method
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper discusses the bootstrap test of entropies. Since the comparison of entropies is of prime interestin applied fields, finding an appropriate way to carry out such a comparison is of the utmost importance. This paperpresents how resampling should be performed to obtain an accurate p-value. Although the test using a pair-wise bootstrapconfidence interval has already been dealt with in some works, here the bootstrap tests are studied because it may demand quite adifferent resampling algorithm compared with the confidence interval. Moreover, the multiple test is studied. The proposed testsappear to yield several appreciable advantages. The easy implementation and the power of the proposed test can be considered asadvantages. Here the entropy of discrete and continuous variables is studied. The proposed tests are examined using Monte Carloinvestigations, and also evaluated using various distributions.

Keyword
Bootstrap method; Entropy; Jackknife; Monte Carlo investigation; Multiple test
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-159210 (URN)
Available from: 2011-09-25 Created: 2011-09-25 Last updated: 2012-02-16
7. On Resampling for the Contingency Table based on Information Energy
Open this publication in new window or tab >>On Resampling for the Contingency Table based on Information Energy
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The bootstrap method is studied herein for the analysis of categorical data,in particular for the contin­gency table. The way to carry out atest of association is to bootstrap on the basis of expected values that havealready been ascertained by a few authors. This paper shows the theoreticalapproach of bootstrapping for a contingency table, and the idea which it isbased on has been inspired by the use of the informational energy func­tion.The properties of the proposed tests are illustrated and discussed using MonteCarlo simulations. The paper ends with analytical examples that elucidate the use ofthe proposed tests.

Keyword
Bootstrap method; Chi-squared test; Contingency table; Informational energy; Monte Carlo investigation
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-158980 (URN)
Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2011-09-25

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