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ravishanker n first course linear model theory 2020

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Textbook in PDF format This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation Contents: Review of Vector and Matrix Algebra Basic definitions and properties Exercises Properties of Special Matrices Partitioned Matrices Algorithms for matrix factorization Symmetric and idempotent matrices Nonnegative definite quadritic forms and matrices Simultaneous diagonalization of matrices Geometrical Perspectives Vector and matrix differentiation Special operations on matrices Linear optimization Exercises Generalized Inverses and Solutions to Linear Systems Generalized inverses Solutions to linear systems Exercises The General Linear Model Model definition and examples The least squares approach Estimable functions Gauss-Markov theorem Generalized least squares Estimation subject to linear restrictions Exercises Multivariate Normal and Related Distributions Multivariate probability distributions Multivariate normal distribution and properties Some noncentral distributions Distributions of quadratic forms Alternatives to multivariate normal distribution Exercises Sampling from the Multivariate Normal Distribution Distribution of sample mean and covariance Distributions related to correlation coefficients Assessing the normality assumption Transformations to approximate normality Exercises Inference for the General Linear Model Properties of least square estimates General linear hypothesis Confidence intervals and multiple comparisons Restricted and reduced models Likelihood based approaches Exercises Multiple Regression Models Departures from model assumptions Model selection in regression Orthogonal and collinear predictors Prediction intervals and calibration Regression diagnostics Dummy variables in regression Robust regression Nonparametric regression methods Exercises Fixed Effects Linear Models Checking model assumptions Inference for unbalanced ANOVA models Analaysis of Covariance Nonparametric procedures Exercises Random-Effects and Mixed-Effects Models One-factor random-effects model Mixed-effects linear models Exercises Special Topics Bayesian linear models Dynamic linear models Longitudinal models Generalized linear models Exercises A Review of Probability Distributions Solutions to Selected Exercises References Author Index Subject Index

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Ravishanker N., Dey D. A First Course in Linear Model Theory 2020.pdf 26.6 MB

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ravishanker n first course linear model theory 2020

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