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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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Structural equation modeling. --- Analysis of covariance. --- Linear models (Statistics) --- Multilevel models (Statistics) --- Hierarchical linear models (Statistics) --- Mixed effects models (Statistics) --- Random coefficient models (Statistics) --- Variance component models (Statistics) --- Mathematical models --- Regression analysis --- Models, Linear (Statistics) --- Mathematical statistics --- Statistics --- Covariance analysis --- SEM (Structural equation modeling) --- Multivariate analysis --- Factor analysis --- Path analysis (Statistics) --- Structural equation modeling --- Analysis of covariance

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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Differentiable dynamical systems. --- Chaotic behavior in systems. --- Stochastic systems. --- Systems, Stochastic --- Stochastic processes --- System analysis --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Affine transformation. --- Amplitude. --- Arbitrarily large. --- Attractor. --- Autocovariance. --- Big O notation. --- Central limit theorem. --- Change of variables. --- Chaos theory. --- Coefficient of variation. --- Compound Probability. --- Computational problem. --- Control theory. --- Convolution. --- Coriolis force. --- Correlation coefficient. --- Covariance function. --- Cross-covariance. --- Cumulative distribution function. --- Cutoff frequency. --- Deformation (mechanics). --- Derivative. --- Deterministic system. --- Diagram (category theory). --- Diffeomorphism. --- Differential equation. --- Dirac delta function. --- Discriminant. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Equations of motion. --- Even and odd functions. --- Excitation (magnetic). --- Exponential decay. --- Extreme value theory. --- Flow velocity. --- Fluid dynamics. --- Forcing (recursion theory). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Frequency domain. --- Gaussian noise. --- Gaussian process. --- Harmonic analysis. --- Harmonic function. --- Heteroclinic orbit. --- Homeomorphism. --- Homoclinic orbit. --- Hyperbolic point. --- Inference. --- Initial condition. --- Instability. --- Integrable system. --- Invariant manifold. --- Iteration. --- Joint probability distribution. --- LTI system theory. --- Limit cycle. --- Linear differential equation. --- Logistic map. --- Marginal distribution. --- Moduli (physics). --- Multiplicative noise. --- Noise (electronics). --- Nonlinear control. --- Nonlinear system. --- Ornstein–Uhlenbeck process. --- Oscillation. --- Parameter space. --- Parameter. --- Partial differential equation. --- Perturbation function. --- Phase plane. --- Phase space. --- Poisson distribution. --- Probability density function. --- Probability distribution. --- Probability theory. --- Probability. --- Production–possibility frontier. --- Relative velocity. --- Scale factor. --- Shear stress. --- Spectral density. --- Spectral gap. --- Standard deviation. --- Stochastic process. --- Stochastic resonance. --- Stochastic. --- Stream function. --- Surface stress. --- Symbolic dynamics. --- The Signal and the Noise. --- Topological conjugacy. --- Transfer function. --- Variance. --- Vorticity.

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The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

Self-similar processes. --- Distribution (Probability theory) --- Processus autosimilaires --- Distribution (Théorie des probabilités) --- 519.218 --- Self-similar processes --- 519.24 --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Selfsimilar processes --- Stochastic processes --- Special stochastic processes --- 519.218 Special stochastic processes --- Distribution (Théorie des probabilités) --- Almost surely. --- Approximation. --- Asymptotic analysis. --- Autocorrelation. --- Autoregressive conditional heteroskedasticity. --- Autoregressive–moving-average model. --- Availability. --- Benoit Mandelbrot. --- Brownian motion. --- Central limit theorem. --- Change of variables. --- Computational problem. --- Confidence interval. --- Correlogram. --- Covariance matrix. --- Data analysis. --- Data set. --- Determination. --- Fixed point (mathematics). --- Foreign exchange market. --- Fractional Brownian motion. --- Function (mathematics). --- Gaussian process. --- Heavy-tailed distribution. --- Heuristic method. --- High frequency. --- Inference. --- Infimum and supremum. --- Instance (computer science). --- Internet traffic. --- Joint probability distribution. --- Likelihood function. --- Limit (mathematics). --- Linear regression. --- Log–log plot. --- Marginal distribution. --- Mathematica. --- Mathematical finance. --- Mathematics. --- Methodology. --- Mixture model. --- Model selection. --- Normal distribution. --- Parametric model. --- Power law. --- Probability theory. --- Publication. --- Random variable. --- Regime. --- Renormalization. --- Result. --- Riemann sum. --- Self-similar process. --- Self-similarity. --- Simulation. --- Smoothness. --- Spectral density. --- Square root. --- Stable distribution. --- Stable process. --- Stationary process. --- Stationary sequence. --- Statistical inference. --- Statistical physics. --- Statistics. --- Stochastic calculus. --- Stochastic process. --- Technology. --- Telecommunication. --- Textbook. --- Theorem. --- Time series. --- Variance. --- Wavelet. --- Website.