Discriminant coordinates analysis for multivariate functional data

Abstract

One of the basic statistical methods of dimensionality reduction is analysis of discriminant coordinates given by Fisher (1936 Fisher, R. A. 1936. The use of multiple measurements in taxonomic problem. Annals of Eugenics 7 (2):179–88. doi:10.1111/j.1469-1809.1936.tb02137.x.[Crossref] , [Google Scholar]) and Rao (1948). The space of discriminant coordinates is a space convenient for presenting multidimensional data originating from multiple groups and for the use of various classification methods (methods of discriminant analysis). In the present paper, we adapt the classical discriminant coordinates analysis to multivariate functional data. The theory has been applied to analysis of textural properties of apples of six varieties, measured over a period of 180?days, stored in two types of refrigeration chamber.     

Estimation of a relative potency of two preparations with correlated responses

Estimation of a relative potency of two preparations in so-called parallel-line assays is presented. A special type of incomplete Latin square designs where doses of preparations are administered is considered. Testing hypotheses about similarity of preparations and their relative potency in the case of correlated observations are regarded. Confidence interval for the relative potency of preparations is also given. Theoretical considerations are applied to point and interval estimation of potencies of new tuberculins with respect to some international standards tested in experiments on guinea-pigs.     

2-Rainbow domination number of Cartesian products: C_{n}\square C_{3} and C_{n}\square C_{5}

A function \(f:V(G)\rightarrow \mathcal P (\{1,\ldots ,k\})\) is called a \(k\) -rainbow dominating function of \(G\) (for short \(kRDF\) of \(G)\) if \( \bigcup \nolimits _{u\in N(v)}f(u)=\{1,\ldots ,k\},\) for each vertex \( v\in V(G)\) with \(f(v)=\varnothing .\) By \(w(f)\) we mean \(\sum _{v\in V(G)}\left|f(v)\right|\) and we call it the weight of \(f\) in \(G.\) The minimum weight of a \( kRDF\) of \(G\) is called the \(k\) -rainbow domination number of \(G\) and it is denoted by \(\gamma _{rk}(G).\) We investigate the \(2\) -rainbow domination number of Cartesian products of cycles. We give the exact value of the \(2\) -rainbow domination number of \(C_{n}\square C_{3}\) and we give the estimation of this number with respect to \(C_{n}\square C_{5},\) \((n\ge 3).\) Additionally, for \(n=3,4,5,6,\) we show that \(\gamma _{r2}(C_{n}\square C_{5})=2n.\)      

Simulation Study on Improved Shapiro–Wilk Tests for Normality

The article concerns tests for normality based on the Shapiro–Wilk W statistic. The constants in the test statistic are recalculated as those given in Shapiro and Wilk are incorrect. The empirical significance levels and power of improved tests have been evaluated in simulation study and compared to original ones. The improved tests were also applied to the multivariate case. In this case, we consider two implementations of the W statistic, the first one proposed by Srivastava and Hui and the other by Hanusz and Tarasinska. Empirical size of tests and their power have been compared to the Henze–Zirkler test.     

Arcs in $$\mathbb Z^2_{2p}$$

An arc in \(\mathbb Z^2_n\) is defined to be a set of points no three of which are collinear. We describe some properties of arcs and determine the maximum size of arcs for some small n.     

A Monte Carlo comparison of Jarque–Bera type tests and Henze–Zirkler test of multivariate normality

In the paper, tests for multivariate normality (MVN) of Jarque-Bera type, based on skewness and kurtosis, have been considered. Tests proposed by Mardia and Srivastava, and the combined tests based on skewness and kurtosis defined by Jarque and Bera have been taken into account. In the Monte Carlo simulations, for each combination of p = 2, 3, 4, 5 number of traits and n = 10(5)50(10)100 sample sizes 10,000 runs have been done to calculate empirical Type I errors of tests under consideration, and empirical power against different alternative distributions. Simulation results have been compared to the Henze–Zirkler’s test. It should be stressed that no test yet proposed is uniformly better than all the others in every combination of conditions examined.     

Striving for Consensus: How Panels Evaluate Artistic Productions

Qualitative Sociology - Researchers have studied how artistic judgments are made in group interactions, but much remains to be known about artistic evaluations in decision-making settings where...