The aim of this paper is to review likelihood ratio test procedures in multivariate linear models, focusing on projection matrices. It is noted that the projection matrices to the spaces spanned by mean vectors in hypothesis and alternatives play an important role. Some basic properties are given for projection matrices. The models treated include multivariate regression model, discriminant ana...

In this paper we investigate the algebraic properties of multivariate discrete splines. It turns out that multivariate discrete splines are closely related to linear diophantine equations. In particular, we use a solvability condition for a system of linear diophantine equations to obtain a necessary and sufficient condition for the integer translates of a discrete box spline to be linearly ind...

Extended Linear Models, Multivariate Splines and ANOVA by Mark Henry Hansen Doctor of Philosophy in Statistics University of California at Berkeley Professor Charles J. Stone, Chair In this dissertation, we pursue a theoretical investigation into several aspects of multivariate function estimation. In general, we con ne ourselves to estimators that are smooth, piecewise polynomial functions, or...

We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of exposure across outcomes. In contrast to the Sammel-Ryan model, the MLMM separates the mean and correlation parameter...

Chromatographic fingerprinting of complex biological samples is an active research area with a large and growing literature. Multivariate statistical and pattern recognition techniques can be effective methods for the analyisis of such complex data. However, the classification of complex samples on the basis of their chromatographic profiles is complicated by two factors: 1) confounding of the ...

investigation of soil properties like cation exchange capacity (cec) plays important roles in study of environmental reaserches as the spatial and temporal variability of this property have been led to development of indirect methods in estimation of this soil characteristic. pedotransfer functions (ptfs) provide an alternative by estimating soil parameters from more readily available soil data...

Temperature time series with high spatial and temporal resolutions are important for several applications. The new MODIS Land Surface Temperature (LST) collection 6 provides numerous improvements compared to collection 5. However, being remotely sensed data in the thermal range, LST shows gaps in cloud-covered areas. We present a novel method to fully reconstruct MODIS daily LST products for ce...