{"title":"Measures of multivariate skewness and kurtosis in high-dimensional framework","authors":"Kazuyuki Koizumi, Takuma Sumikawa, T. Pavlenko","doi":"10.55937/sut/1424858950","DOIUrl":"https://doi.org/10.55937/sut/1424858950","url":null,"abstract":"Skewness and kurtosis characteristics of a multivariate p-dimensional distribution introduced by Mardia (1970) have been used in various testing procedures and demonstrated attractive asymptotic properties in large sample settings. However these characteristics are not designed for high-dimensional problems where the dimensionality, p can largely exceeds the sample size, N. Such type of high-dimensional data are commonly encountered in modern statistical applications. This the suggests that new measures of skewness and kurtosis that can accommodate high-dimensional settings must be derived and carefully studied. In this paper, we show that, by exploiting the dependence structure, new expressions for skewness and kurtosis are introduced as an extension of the corresponding Mardia’s measures, which uses the potential advantages that the block-diagonal covariance structure has to offer in high dimensions. Asymptotic properties of newly derived measures are investigated and the cumulant based characterizations are presented along with of applications to a mixture of multivariate normal distributions and multivariate Laplace distribution, for which the explicit expressions of skewness and kurto-sis are obtained. Test statistics based on the new measures of skewness and kurtosis are proposed for testing a distribution shape, and their limit distributions are established in the asymptotic framework where N → ∞ and p is fixed but large, including p > N. For the dependence structure learning, the gLasso based technique is explored followed by AIC step which we propose for optimization of the gLasso candidate model. Performance accuracy of the test procedures based on our estimators of skewness and kurtosis are evaluated using Monte Carlo simulations and the validity of the suggested approach is shown for a number of cases when p > N.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89354298","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}
{"title":"Harmonic maps in almost contact geometry","authors":"J. Inoguchi","doi":"10.55937/sut/1424965327","DOIUrl":"https://doi.org/10.55937/sut/1424965327","url":null,"abstract":"","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73589567","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}
{"title":"Inequalities for Power Series in Banach Algebras","authors":"S. Dragomir","doi":"10.55937/sut/1415034196","DOIUrl":"https://doi.org/10.55937/sut/1415034196","url":null,"abstract":"for any a; b 2 B: The normed algebra (B; k k) is a Banach algebra if k k is a complete norm. We assume that the Banach algebra is unital, this means that B has an identity 1 and that k1k = 1: Let B be a unital algebra. An element a 2 B is invertible if there exists an element b 2 B with ab = ba = 1: The element b is unique; it is called the inverse of a and written a 1 or 1 a : The set of invertible elements of B is denoted by InvB. If a; b 2InvB then ab 2InvB and (ab) 1 = b a : For a unital Banach algebra we also have: (i) If a 2 B and limn!1 kank < 1; then 1 a 2InvB; (ii) fa 2 B: k1 bk < 1g InvB; (iii) InvB is an open subset of B; (iv) The map InvB 3 a 7 ! a 1 2InvB is continuous. For simplicity, we denote 1; where 2 C and 1 is the identity of B, by : The resolvent set of a 2 B is de\u0085ned by","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"220 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72639648","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}
{"title":"On units of a family of cubic number fields","authors":"K. Kaneko","doi":"10.55937/sut/1415033670","DOIUrl":"https://doi.org/10.55937/sut/1415033670","url":null,"abstract":"We nd the fundamental units of a family of cubic elds introduced by Ishida. Using the family, we also construct a family of biquadratic elds whose 3-class eld tower has length greater than 1. AMS 2010 Mathematics Subject Classication. 11R16, 11R27.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77794695","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}
{"title":"Single and multiple comparison procedures for partial covariance matrices of two treatment groups in clinical trials","authors":"Y. Nakazuru, T. Seo","doi":"10.55937/sut/1415120761","DOIUrl":"https://doi.org/10.55937/sut/1415120761","url":null,"abstract":"","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78873685","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}
{"title":"On the existence of a regular factorial subring and a p-basis of a polynomial ring in two variables in characteristic p=3","authors":"T. Ono","doi":"10.55937/sut/1415457453","DOIUrl":"https://doi.org/10.55937/sut/1415457453","url":null,"abstract":"","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89675906","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}
{"title":"Some transformations on Kenmotsu manifolds","authors":"A. Shaikh, F. Al-Solamy, H. Ahmad","doi":"10.55937/sut/1393589346","DOIUrl":"https://doi.org/10.55937/sut/1393589346","url":null,"abstract":"","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74828801","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}
{"title":"Sum-symmetry model and its orthogonal decomposition for square contingency tables with ordered categories","authors":"K. Yamamoto, Yayoi Tanaka, S. Tomizawa","doi":"10.55937/sut/1393504838","DOIUrl":"https://doi.org/10.55937/sut/1393504838","url":null,"abstract":"","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"112 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77257451","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}
{"title":"R(p,q)-calculus: differentiation and integration","authors":"M. N. Hounkonnou","doi":"10.55937/sut/1394548362","DOIUrl":"https://doi.org/10.55937/sut/1394548362","url":null,"abstract":"We build a framework for R(p;q)-deformed calculus, which pro- vides a method of computation for deformed R(p;q)-derivative and integration, generalizing known deformed derivatives and integrations of analytic functions defined on a complex disc as particular cases corresponding to conveniently cho- sen meromorphic functions. Under prescribed conditions, we define the R(p;q)- derivative and integration. Relevant examples are also given.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91223508","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}
{"title":"Even vertex odd mean labeling of graphs","authors":"R. Vasuki, A. Nagarajan, S. Arockiaraj","doi":"10.55937/sut/1394108286","DOIUrl":"https://doi.org/10.55937/sut/1394108286","url":null,"abstract":"In this paper we introduce a new type of labeling known as even vertex odd mean labeling. A graph G with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f : V (G) → {0, 2, 4, . . . , 2q−2, 2q} such that the induced map f∗ : E(G) → {1, 3, 5, . . . , 2q− 1} defined by f∗(uv) = f(u)+f(v) 2 is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. Here we investigate the even vertex odd mean behaviour of some standard graphs. AMS 2010 Mathematics Subject Classification. 05C.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75785158","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}