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Multivariate Normality (multivariate + normality)

Distribution by Scientific Domains

Life Sciences	50%

Selected Abstracts

An Omnibus Test for Univariate and Multivariate Normality,

OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2008
Jurgen A. Doornik
Abstract We suggest a convenient version of the omnibus test for normality, using skewness and kurtosis based on Shenton and Bowman [Journal of the American Statistical Association (1977) Vol. 72, pp. 206,211], which controls well for size, for samples as low as 10 observations. A multivariate version is introduced. Size and power are investigated in comparison with four other tests for multivariate normality. The first power experiments consider the whole skewness,kurtosis plane; the second use a bivariate distribution which has normal marginals. It is concluded that the proposed test has the best size and power properties of the tests considered. [source]

Gamma regression improves Haseman-Elston and variance components linkage analysis for sib-pairs

GENETIC EPIDEMIOLOGY, Issue 2 2004
Mathew J. Barber
Abstract Existing standard methods of linkage analysis for quantitative phenotypes rest on the assumptions of either ordinary least squares (Haseman and Elston [1972] Behav. Genet. 2:3,19; Sham and Purcell [2001] Am. J. Hum. Genet. 68:1527,1532) or phenotypic normality (Almasy and Blangero [1998] Am. J. Hum. Genet. 68:1198,1199; Kruglyak and Lander [1995] Am. J. Hum. Genet. 57:439,454). The limitations of both these methods lie in the specification of the error distribution in the respective regression analyses. In ordinary least squares regression, the residual distribution is misspecified as being independent of the mean level. Using variance components and assuming phenotypic normality, the dependency on the mean level is correctly specified, but the remaining residual coefficient of variation is constrained a priori. Here it is shown that these limitations can be addressed (for a sample of unselected sib-pairs) using a generalized linear model based on the gamma distribution, which can be readily implemented in any standard statistical software package. The generalized linear model approach can emulate variance components when phenotypic multivariate normality is assumed (Almasy and Blangero [1998] Am. J. Hum Genet. 68: 1198,1211) and is therefore more powerful than ordinary least squares, but has the added advantage of being robust to deviations from multivariate normality and provides (often overlooked) model-fit diagnostics for linkage analysis. Genet Epidemiol 26:97,107, 2004. © 2004 Wiley-Liss, Inc. [source]

One class classifiers for process monitoring illustrated by the application to online HPLC of a continuous process

JOURNAL OF CHEMOMETRICS, Issue 3-4 2010
Sila Kittiwachana
Abstract In process monitoring, a representative out-of-control class of samples cannot be generated. Here, it is assumed that it is possible to obtain a representative subset of samples from a single ,in-control class' and one class classifiers namely Q and D statistics (respectively the residual distance to the disjoint PC model and the Mahalanobis distance to the centre of the QDA model in the projected PC space), as well as support vector domain description (SVDD) are applied to disjoint PC models of the normal operating conditions (NOC) region, to categorise whether the process is in-control or out-of-control. To define the NOC region, the cumulative relative standard deviation (CRSD) and a test of multivariate normality are described and used as joint criteria. These calculations were based on the application of window principal components analysis (WPCA) which can be used to define a NOC region. The D and Q statistics and SVDD models were calculated for the NOC region and percentage predictive ability (%PA), percentage model stability (%MS) and percentage correctly classified (%CC) obtained to determine the quality of models from 100 training/test set splits. Q, D and SVDD control charts were obtained, and 90% confidence limits set up based on multivariate normality (D and Q) or SVDD D value (which does not require assumptions of normality). We introduce a method for finding an optimal radial basis function for the SVDD model and two new indices of percentage classification index (%CI) and percentage predictive index (%PI) for non-NOC samples are also defined. The methods in this paper are exemplified by a continuous process studied over 105.11,h using online HPLC. Copyright © 2010 John Wiley & Sons, Ltd. [source]

An Omnibus Test for Univariate and Multivariate Normality,

Regression-based Multivariate Linkage Analysis with an Application to Blood Pressure and Body Mass Index

ANNALS OF HUMAN GENETICS, Issue 1 2007
T. Wang
Summary Multivariate linkage analysis has been suggested for the analysis of correlated traits, such as blood pressure (BP) and body mass index (BMI), because it may offer greater power and provide clearer results than univariate analyses. Currently, the most commonly used multivariate linkage methods are extensions of the univariate variance component model. One concern about those methods is their inherent sensitivity to the assumption of multivariate normality which cannot be easily guaranteed in practice. Another problem possibly related to all multivariate linkage analysis methods is the difficulty in interpreting nominal p-values, because the asymptotic distribution of the test statistic has not been well characterized. Here we propose a regression-based multivariate linkage method in which a robust score statistic is used to detect linkage. The p-value of the statistic is evaluated by a simple and rapid simulation procedure. Theoretically, this method can be used for any number and type of traits and for general pedigree data. We apply this approach to a genome linkage analysis of blood pressure and body mass index data from the Beaver Dam Eye Study. [source]