Search results for "Matrices"

MR2896126 Selmanogullari, T.; Savas, E.; Rhoades, B. E. On $q$-Hausdorff matrices. Taiwanese J. Math. 15 (2011), no. 6, 2429--2437

2011

Differences in achievement not in intelligence in the north and south of Italy: Comments on

2012

Abstract Lynn (2010a, 2010b) argued that individuals from south Italy have a lower IQ than individuals from north Italy, and that these differences in IQ are at the basis of north–south gap in income, education, infant mortality, stature, and literacy. In the present paper, we discuss several theoretical and methodological aspects which we regard as flaws of Lynn's studies. Moreover, we report scores of southern Italian children on Raven's Progressive Matrices and a north–south comparison for the PASS theory of intelligence as measured by the Cognitive Assessment System (Taddei & Naglieri, 2006). Both results reveal similar levels of performance of northern and southern Italian children in …

Relationship between socioeconomic factors and intelligence of preschoolers: A cohort study in the Serbian context

2020

The aim of the current research is to analyse the relationship between the socioeconomic status (SES) of parents and intellectual abilities (IQ) of preschool children of Serbian territory, and in particular how SES factors relate to preschool children’s IQ measured with Raven’s Coloured Progressive Matrices (CPM), in the different age groups. The research included 430 parents and 430 preschool children. A confirmatory factor analysis of the SES questionnaire revealed five factors: educational and professional status of father and mother, residential and educational status of the family, sport status of parents and comfort of family housing. No gender differences in IQ levels were found in c…

The rank of random regular digraphs of constant degree

2018

Abstract Let d be a (large) integer. Given n ≥ 2 d , let A n be the adjacency matrix of a random directed d -regular graph on n vertices, with the uniform distribution. We show that the rank of A n is at least n − 1 with probability going to one as n grows to infinity. The proof combines the well known method of simple switchings and a recent result of the authors on delocalization of eigenvectors of A n .

Sign and rank covariance matrices

2000

The robust estimation of multivariate location and shape is one of the most challenging problems in statistics and crucial in many application areas. The objective is to find highly efficient, robust, computable and affine equivariant location and covariance matrix estimates. In this paper, three different concepts of multivariate sign and rank are considered and their ability to carry information about the geometry of the underlying distribution (or data cloud) are discussed. New techniques for robust covariance matrix estimation based on different sign and rank concepts are proposed and algorithms for computing them outlined. In addition, new tools for evaluating the qualitative and quant…

The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies

2003

We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform …

Estimates of Regression Coefficients Based on the Sign Covariance Matrix

2002

SummaryA new estimator of the regression parameters is introduced in a multivariate multiple-regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the SCM regression estimate. The estimate is shown to be consistent with a limiting multinormal distribution. The influence function, as a function of the length of the contamination vector, is shown to be linea…

Maximum likelihood estimation for the exponential power function parameters

1995

This paper addresses the problem of obtaining maximum likelihood estimates for the three parameters of the exponential power function; the information matrix is derived and the covariance matrix is here presented; the regularity conditions which ensure asymptotic normality and efficiency are examined. A numerical investigation is performed for exploring the bias and variance of the maximum likelihood estimates and their dependence on sample size and shape parameter.

The smallest singular value of a shifted $d$-regular random square matrix

2017

We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. Specifically, let $$C_1<d< c n/\log ^2 n$$ and let $$\mathcal {M}_{n,d}$$ be the set of all $$n\times n$$ square matrices with 0 / 1 entries, such that each row and each column of every matrix in $$\mathcal {M}_{n,d}$$ has exactly d ones. Let M be a random matrix uniformly distributed on $$\mathcal {M}_{n,d}$$ . Then the smallest singular value $$s_{n} (M)$$ of M is greater than $$n^{-6}$$ with probability at least $$1-C_2\log ^2 d/\sqrt{d}$$ , where c, $$C_1$$ , and $$C_2$$ are absolute positive constants independent of any other parameter…

Linear Recursive Equations, Covariance Selection, and Path Analysis

1980

Abstract By defining a reducible zero pattern and by using the concept of multiplicative models, we relate linear recursive equations that have been introduced by econometrician Herman Wold (1954) and path analysis as it was proposed by geneticist Sewall Wright (1923) to the statistical theory of covariance selection formulated by Arthur Dempster (1972). We show that a reducible zero pattern is the condition under which parameters as well as least squares estimates in recursive equations are one-to-one transformations of parameters and of maximum likelihood estimates, respectively, in a decomposable covariance selection model. As a consequence, (a) we can give a closed-form expression for t…