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Traditional approaches to ANOVA and ANCOVA are now being replaced by a General Linear Modeling (GLM) approach. This book begins with a brief history of the separate development of ANOVA and regression analyses and demonstrates how both analysis forms are subsumed by the General Linear Model. A simple single independent factor ANOVA is analysed first in conventional terms and then again in GLM terms to illustrate the two approaches. The text then goes on to cover the main designs, both independent and related ANOVA and ANCOVA, single and multi-factor designs. The conventional

Regression analysis. --- Social sciences -- Statistical methods. --- Analysis of variance --- Analysis of covariance --- Covariance analysis --- Regression analysis --- ANOVA (Analysis of variance) --- Variance analysis --- Mathematical statistics --- Experimental design

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Linear Models: An Integrated Approach aims to provide a clearand deep understanding of the general linear model using simplestatistical ideas. Elegant geometric arguments are also invoked asneeded and a review of vector spaces and matrices is provided to makethe treatment self-contained.

Linear models (Statistics) --- Analysis of covariance. --- Regression analysis. --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- Covariance analysis --- Regression analysis --- Models, Linear (Statistics) --- Mathematical models --- Mathematical statistics --- Statistics --- Modèles linéaires (Statistique)

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This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with non-random predictors in a finite-dimensional setting. This approach is more insightful, more elegant, more direct, and simpler than the more common matrix approach to linear regression, analysis of variance, and analysis of covariance models in statistics. The book discusses the intuition behind and optimal properties of various methods of estimating and testing hypotheses about unknown parameters in the models. Topics covered range from linear algebra, such as inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and non-optimal properties of Gauss-Markov, Bayes, and shrinkage estimators under assumption of normality, the optimal properties of F-test, and the analysis of covariance and missing observations.

Linear models (Statistics) --- Analysis of variance --- Regression Analysis --- Analysis of covariance --- Analysis of variance. --- Regression analysis. --- Analysis of covariance. --- Covariance analysis --- Regression analysis --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- ANOVA (Analysis of variance) --- Variance analysis --- Mathematical statistics --- Experimental design --- Models, Linear (Statistics) --- Mathematical models --- Statistics --- Mathematical Sciences --- Probability

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The central object of the book is a subtle scalar Riemannian curvature quantity in even dimensions which is called Branson’s Q-curvature. It was introduced by Thomas Branson about 15 years ago in connection with an attempt to systematise the structure of conformal anomalies of determinants of conformally covariant differential operators on Riemannian manifolds. Since then, numerous relations of Q-curvature to other subjects have been discovered, and the comprehension of its geometric significance in four dimensions was substantially enhanced through the studies of higher analogues of the Yamabe problem. The book attempts to reveal some of the structural properties of Q-curvature in general dimensions. This is achieved by the development of a new framework for such studies. One of the main properties of Q-curvature is that its transformation law under conformal changes of the metric is governed by a remarkable linear differential operator: a conformally covariant higher order generalization of the conformal Laplacian. In the new approach, these operators and the associated Q-curvatures are regarded as derived quantities of certain conformally covariant families of differential operators which are naturally associated to hypersurfaces in Riemannian manifolds. This method is at the cutting edge of several central developments in conformal differential geometry in the last two decades such as Fefferman-Graham ambient metrics, spectral theory on Poincaré-Einstein spaces, tractor calculus, and Cartan geometry. In addition, the present theory is strongly inspired by the realization of the idea of holography in the AdS/CFT-duality. This motivates the term holographic descriptions of Q-curvature.

Analysis of covariance. --- Curvature. --- Differential operators. --- Geometry, Riemannian. --- Geometry, Riemannian --- Curvature --- Differential operators --- Analysis of covariance --- Mathematics --- Geometry --- Physical Sciences & Mathematics --- Riemann geometry --- Riemannian geometry --- Covariance analysis --- Operators, Differential --- Mathematics. --- Topological groups. --- Lie groups. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Differential geometry. --- Physics. --- Differential Geometry. --- Topological Groups, Lie Groups. --- Global Analysis and Analysis on Manifolds. --- Mathematical Methods in Physics. --- Regression analysis --- Differential equations --- Operator theory --- Calculus --- Curves --- Surfaces --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Global differential geometry. --- Topological Groups. --- Global analysis. --- Mathematical physics. --- Physical mathematics --- Physics --- Groups, Topological --- Continuous groups --- Geometry, Differential --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Differential geometry --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Topology

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Evapotranspiration (ET) is a critical component of the water and energy balances, and the number of remote sensing-based ET products and estimation methods has increased in recent years. Various aspects of remote sensing of ET are reported in the 11 papers published in this book. The major research areas covered by this book include inter-comparison and performance evaluation of widely used one- and two-source energy balance models, a new dual-source model (Soil Plant Atmosphere and Remote Sensing Evapotranspiration, SPARSE), and a process-based model (ETMonitor); assessment of multi-source (e.g., remote sensing, reanalysis, and land surface model) ET products; development or improvement of data fusion frameworks to predict continuous daily ET at a high spatial resolution (field-scale or 30 m) by fusing the advanced spaceborne thermal emission reflectance radiometer (ASTER), the moderate resolution imaging spectroradiometer (MODIS), and Landsat data; and investigating uncertainties in ET estimates using an ET ensemble composed of several land surface models and diagnostic datasets. The effects of the differences between ET products on water resources and ecosystem management were also investigated. More accurate ET estimates and improved understanding of remotely sensed ET products are crucial for maximizing crop productivity while minimizing water losses and management costs.

Eddy-covariance --- surface energy balance model --- evapotranspiration --- Oklahoma Mesonet --- Chi river basin --- SADFAET --- a stratification method --- ecosystem management --- process-based model --- heterogeneous conditions --- land surface temperature --- ETMonitor --- model --- latent heat flux --- multi-source --- water resources management --- remote sensing --- ET --- fusion --- Google Earth Engine --- water stress --- component temperature decomposition --- data fusion --- Mun river basin --- Murrumbidgee River catchment --- remote-sensing --- Thailand --- uncertainty --- field-scale --- partition --- land surface model --- two-source energy balance model --- Surface Energy Balance System --- China --- evapotranspiration partitioning --- yield --- calibration --- unmixing-based method --- Landsat 8 --- eddy covariance observations --- METRIC --- MODIS --- surface energy balance algorithm for land (SEBAL) --- West Africa --- MPDI-integrated SEBS --- STARFM --- multi-source satellite data