
Loc Nguyen (2013, July 26). A new method to determine separated hyperplane for nonparametric sign test in multivariate data
Type

Journal Article

Abstract

Nonparametric testing is very necessary in case that the statistical sample does not conform normal distribution or we have no knowledge about sample distribution. Sign test is a popular and effective test for nonparametric model but it cannot be applied into multivariate data in which observations are vectors because the ordering and comparative operators are not defined in ndimension vector space. So, this research proposes a new approach to perform sign test on multivariate sample by using a hyperplane to separate multidimensional observations into two sides. Therefore, it is possible for the sign test to assign plus signs and minus signs to observations in each side. Moreover, this research introduces a new method to determine the separated hyperplane. This method is a variant of support vector machine (SVM), thus, the optimized hyperplane is the one that contains null hypothesis and splits observations as discriminatively as possible.
Keywords: separated hyperplane, nonparametric sign test.

Accepted

Journal of Mathematics and System Science. Acceptance date is July 26, 2013.
ISSN online: 21595305, ISSN print: 21595291, Open Access.
Editors: Assia GuezaneLakoud, William P. Fox, Elisa Francomano, Sergo A. Episkoposian, Elizbar Nadaraya, Alexander Nikolaevich Raikov, Baha ŞEN, Claudio Cuevas, Wattanavadee Sriwattanapongse, Mohammad Mehdi Rashidi.
Publisher: David Publishing Company, USA.
Contact: David Publishing Company, 1840 Industrial Drive, Suite 160, Libertyville, IL 60048, USA.
Website: http://www.davidpublisher.org/Home/Journal/JMSS
Tel: 13239847526, 3234101082; Fax: 13239847374
Email: order@davidpublishing.com

Presented

Statistics and its interactions with other disciplines (SIOD 2013), organized by the University of Moncton (Canada), together with The University of Science of Hochiminh City, Ton Duc Thang University, The University of Economics and Law of Ho Chi Minh city and Can Tho University, all located in Vietnam.
Place and date: Ton Duc Thang University, Ho Chi Minh city, Vietnam. June 57, 2013.
Website: http://siod.tdt.edu.vn/index.php/siod/2013
Email: phamgit@umoncton.ca or cdkhanh@itam.tdt.edu.vn

Identifiers


Links


Citations

Nguyen, L. (2013, July 26). A new method to determine separated hyperplane for nonparametric sign test in multivariate data. (A. GuezaneLakoud, W. P. Fox, E. Francomano, S. A. Episkoposian, E. Nadaraya, A. N. Raikov, et al., Eds.) Journal of Mathematics and System Science.

Cited


Indexed

Academic Keys, BASE, CEPS, CQVIP, CSTJ, CiteFactor, CSA, DBH, EBSCO, EZB, getCITED, Google Scholar, Index Copernicus, InfoBase Index, InnoSpace, NSD, OCLC, Open JGate, PAIS, PBN, ProQuest, Scholar Steer, SHERPA, SIS, SJournal Index, Summon Serials Solutions, Turkish Education Index, UCSD, UDL, UlrichsWeb, WZB

Metrics


Categories

Statistics, Mathematics


Loc Nguyen (2013, July 22). A Maximum Likelihood Mixture Approach for Multivariate Hypothesis Testing in case of Incomplete Data
Type

Journal Article

Abstract

Multivariate hypothesis testing becomes more and more necessary when data is in the process of changing from scalar and univariate format to multivariate format, especially financial and biological data is often constituted of ndimension vectors. Likelihood ratio test is the best method that applies the test on mean of multivariate sample with known or unknown covariance matrix but it is impossible to use likelihood ratio test in case of incomplete data when the data incompletion gets popular because of many reasons in reality. Therefore, this research proposes a new approach that gives an ability to apply likelihood ratio test into incomplete data. Instead of replacing missing values in incomplete sample by estimated values, this approach classifies incomplete sample into groups and each group is represented by a potential or partial distribution. All partial distributions are unified into a mixture model which is optimized via expectation maximization (EM) algorithm. Finally, likelihood ratio test is performed on mixture model instead of incomplete sample. This research provides a thorough description of proposed approach and mathematical proof that is necessary to such approach. The comparison of mixture model approach and filling missing values approach is also discussed in this research.
Keywords: maximum likelihood, mixture model, multivariate hypothesis testing, incomplete data.

Accepted

Journal of Mathematics and System Science. Acceptance date is July 22, 2013.
ISSN online: 21595305, ISSN print: 21595291, Open Access.
Editors: Assia GuezaneLakoud, William P. Fox, Elisa Francomano, Sergo A. Episkoposian, Elizbar Nadaraya, Alexander Nikolaevich Raikov, Baha ŞEN, Claudio Cuevas, Wattanavadee Sriwattanapongse, Mohammad Mehdi Rashidi.
Publisher: David Publishing Company, USA.
Contact: David Publishing Company, 1840 Industrial Drive, Suite 160, Libertyville, IL 60048, USA.
Website: http://www.davidpublisher.org/Home/Journal/JMSS
Tel: 13239847526, 3234101082; Fax: 13239847374
Email: order@davidpublishing.com

Identifiers


Links


Citations

Nguyen, L. (2013, July 22). A Maximum Likelihood Mixture Approach for Multivariate Hypothesis Testing in case of Incomplete Data. (A. GuezaneLakoud, W. P. Fox, E. Francomano, S. A. Episkoposian, E. Nadaraya, A. N. Raikov, et al., Eds.) Journal of Mathematics and System Science.

Cited


Indexed

Academic Keys, BASE, CEPS, CQVIP, CSTJ, CiteFactor, CSA, DBH, EBSCO, EZB, getCITED, Google Scholar, Index Copernicus, InfoBase Index, InnoSpace, NSD, OCLC, Open JGate, PAIS, PBN, ProQuest, Scholar Steer, SHERPA, SIS, SJournal Index, Summon Serials Solutions, Turkish Education Index, UCSD, UDL, UlrichsWeb, WZB

Metrics


Categories

Statistics


Loc Nguyen (2013, July 17). Nonparametric Hypothesis Testing Report
Type

Report

Abstract

This report is the brief survey of nonparametric hypothesis testing. It includes four main sections about hypothesis testing, one additional section discussing goodnessoffit and conclusion section.
 Sign test section gives an overview of nonparametric testing, which begins with the test on sample median without assumption of normal distribution.
 Signedrank test section and ranksum test section concern improvements of sign test. The prominence of signedrank test is to be able to test sample mean based on the assumption about symmetric distribution. Ranksum test discards the task of assigning and counting plus signs and so it is the most effective method among ranking test methods.
 Nonparametric ANOVA section discusses application of analysis of variance (ANOVA) in nonparametric model. ANOVA is useful to compare and evaluate various data samples at the same time.
 Nonparametric goodnessfittest section, an additional section, focuses on different hypothesis, which measure the distribution similarity between two samples. It determines whether two samples have the same distribution without concerning how the form of distribution is.
 The last section is the conclusion.
Note that in this report terms sample and data sample have the same meaning. A sample contains many data points. Each data point is also called an observation.

Accepted

Science Journal Of Mathematics and Statistics (SJMS). Acceptance date is July 17, 2013.
ISSN: 22766324, Open Access.
Publisher: Science Journal Publication.
Contact: Science Journal Publication, No 4 Vision Street, Off Government Hospital Road, P.O. Box 669, Warri, Delta State, Nigeria.
Website: http://www.sjpub.org/sjms.html
Tel: +2348067669533
Email: info@sjpub.org

Awarded

Certified by Science Journal Publication

Identifiers


Links


Citations

Nguyen, L. (2013, July 17). Nonparametric Hypothesis Testing Report. Vietnam Institute of Mathematics. Warri, Delta State, Nigeria: Science Journal Publication.

Cited


Indexed

CrossRef, Gale, Google Scholar, Summon Serials Solutions, UlrichsWeb

Metrics


Categories

Statistics

Last updated November 2016
Abstracting and indexing
