Titlebook: Linear Model Theory; With Examples and Ex Dale L. Zimmerman Textbook 2020 Springer Nature Switzerland AG 2020 62J05, 62J10, 62F03, 62F10, 6

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risks of acquiring intraoperative neurological deficits, shortens operating time, and lowers the costs of medical care and rehabilitation. It can also reduce the risks of medical malpractice suits and serve as a research tool to better understand nervous system disorders and promote improved treatm

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A Brief Introduction,onal units.” We refer to . as the . (regardless of whether it actually makes sense to think of . as a response to anything) and to .., …, .. as the . (regardless of whether they actually help to explain anything). Let .., .., .., …, .. represent the observed values of these variables for the .th obs

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Selected Matrix Algebra Topics and Results,ge of matrix algebra useful for linear models. That is the objective of this chapter. Admittedly, the topics and results selected for inclusion here are severely abridged, being limited almost exclusively to what will actually be needed in later chapters. Furthermore, for some of the results (partic

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Generalized Inverses and Solutions to Systems of Linear Equations,for other purposes as well, we need to solve various systems of linear equations of the general form . Here . is a specified . × . matrix called the ., . is a specified .-vector called the ., and . is an .-vector of unknowns. Any vector of unknowns that satisfies the system is called a .. A solution

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Types of Linear Models,tional assumptions made about . (i.e., additional to . being nonrandom and known and . being nonrandom and unknown) as the model’s mean structure, and to any additional assumptions made about . [i.e., additional to E(.) = .] as the model’s error structure. In this chapter, we give a brief overview o

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Estimability,t rather to learn whether it is even . to “sensibly estimate” those parameters or functions. Precisely what is meant by “sensibly estimate”? Several definitions are possible, but in this book the phrase is synonymous with “estimate unbiasedly.” Parameters, or functions thereof, that can be estimated

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,Least Squares Estimation for the Gauss–Markov Model,em. This chapter presents the estimation method known as .. Least squares estimation involves finding a value of . that minimizes the distance between . and ., as measured by the squared length of the vector . −.. Although this seems like it should lead to reasonable estimators of the elements of .,

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