Estimation of parameters in the extended growth curve model with a linearly structured covariance matrix

In this paper the extended growth curve model with two terms and a linearly structured covariance matrix is considered. We propose an estimation procedure that handles linearly structured covariance matrices. The idea is first to estimate the covariance matrix when finding the inner product in a regression space and thereafter re-estimate it when it should be interpreted as a dispersion matrix. This idea is exploited by decomposing the residual space, the orthogonal complement to the design space, into three orthogonal subspaces. Studying residuals obtained from projections of observations on these subspaces yields explicit consistent estimators of the covariance matrix. An explicit consistent estimator of the mean is also proposed and numerical examples are given

An Edgeworth-type expansion for the distribution of a likelihood-based discriminant function

The exact distribution of a classification function is often complicated to allow for easy numerical calculations of misclassification errors. The use of expansions is one way of dealing with this difficulty. In this paper, approximate probabilities of misclassification of the maximum likelihood-based discriminant function are established via an Edgeworth-type expansion based on the standard normal distribution for discriminating between two multivariate normal populations

Moments of the likelihood-based discriminant function

The likelihood approach used in this paper leads to quadratic discriminant functions. Classification into one of two known multivariate normal populations with a known and unknown covariance matrix are separately considered, where the two cases depend on the sample size and an unknown squared Mahalanobis distance. Their exact distributions are complicated to obtain. Therefore, moments for the likelihood based discriminant functions are established to express the basic characteristics of respective distribution

Количественные критерии гигиенической оценки воздействия на организм многокомпонентного загрязнения атмосферного воздуха

ВОЗДУХВОЗДУХА ЗАГРЯЗНИТЕЛИизоэффективные концентрацииэксперименты на животныхазота диоксидсеры диоксидАЗОТА ОКСИДЫ /вред воз

Strategisk regnskapsanalyse og verdsettelse av Hjellegjerde ASA

Formålet med denne utredningen har vært å finne et anslag på verdien av Hjellegjerde ved hjelp av en fundamental verdsettelsesmodell. Verdsettelsen er basert på ekstern informasjon og den kunnskapen vi har tilegnet oss gjennom siviløkonomstudiet. Utredningen er delt inn i sju kapitler. I første kapittel gir vi en disposisjon over utredningen. Det andre kapittelet inneholder en presentasjon av Hjellegjerde, og kapittel tre omfatter en strategisk analyse, det vil si både en eksternanalyse og en internanalyse. Regnskapsanalysen i kapittel fire består av omgruppering, analyse og justering av målefeil og forholdstallsanalyse. Basert på den strategiske analysen og regnskapsanalysen utarbeider vi et fremtidsregnskap. I kapittel seks benytter vi fundamental verdsettelse til å komme frem til et verdiestimat på Hjellegjerdeaksjen. Estimatet er usikkert og kapittelet består derfor også av sensitivitetsanalyse. Vi avslutter oppgaven med kapittel sju, hvor vi oppsummerer og konkluderer

Recent developments in multivariate and random matrix analysis: Festschrift in honour of Dietrich von Rosen

This volume is a tribute to Professor Dietrich von Rosen on the occasion of his 65th birthday. It contains a collection of twenty original papers. The contents of the papers evolve around multivariate analysis and random matrices with topics such as high-dimensional analysis, goodness-of-fit measures, variable selection and information criteria, inference of covariance structures, the Wishart distribution and growth curve models.

Closed Form of the Asymptotic Spectral Distribution of Random Matrices Using Free Independence

The spectral distribution function of random matrices is an information-carrying object widely studied within Random matrix theory. Random matrix theory is the main eld placing its research interest in the diverse properties of matrices, with a particular emphasis placed on eigenvalue distribution. The aim of this article is to point out some classes of matrices, which have closed form expressions for the asymptotic spectral distribution function. We consider matrices, later denoted by , which can be decomposed into the sum of asymptotically free independent summands. Let  be a probability space. We consider the particular example of a non-commutative space, where  denotes the set of all   random matrices, with entries which are com-plex random variables with finite moments of any order and  is tracial functional. In particular, explicit calculations are performed in order to generalize the theorem given in [15] and illustrate the use of asymptotic free independence to obtain the asymptotic spectral distribution for a particular form of matrix. Finally, the main result is a new theorem pointing out classes of the matrix  which leads to a closed formula for the asymptotic spectral distribution. Formulation of results for matrices with inverse Stieltjes transforms, with respect to the composition, given by a ratio of 1st and 2nd degree polynomials, is provided

Closed Form of the Asymptotic Spectral Distribution of Random Matrices Using Free Independence

The spectral distribution function of random matrices is an information-carrying object widely studied within Random matrix theory. Random matrix theory is the main eld placing its research interest in the diverse properties of matrices, with a particular emphasis placed on eigenvalue distribution. The aim of this article is to point out some classes of matrices, which have closed form expressions for the asymptotic spectral distribution function. We consider matrices, later denoted by , which can be decomposed into the sum of asymptotically free independent summands. Let  be a probability space. We consider the particular example of a non-commutative space, where  denotes the set of all   random matrices, with entries which are com-plex random variables with finite moments of any order and  is tracial functional. In particular, explicit calculations are performed in order to generalize the theorem given in [15] and illustrate the use of asymptotic free independence to obtain the asymptotic spectral distribution for a particular form of matrix. Finally, the main result is a new theorem pointing out classes of the matrix  which leads to a closed formula for the asymptotic spectral distribution. Formulation of results for matrices with inverse Stieltjes transforms, with respect to the composition, given by a ratio of 1st and 2nd degree polynomials, is provided