Customer Reviews

Matrix Algebra (Econometric Exercises)

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I have used this book as the source of inspiration for the introductory/background part of my doctorate level multivariate class when I was covering the foundations of matrix theory, this way and out. MANOVA and discriminant analysis are about the spectrum of W^{-1} B -- here are exercises on inverses, spectral decomposition, and traces. Marginal and conditional distributions of a multivariate normal are themselves normal -- here are block matrix results for inverses and such that those normality theorems are based on. Effects of non-normality come from the higher order moments -- here are Kronecker products to define those moments, and duplication matrices to deal with redundant elements. You want to see the effects of non-normality on your PCA or SEM procedures -- here are the matrix calculus results, the foundations of the matrix version of the delta method.

I won't be repeating the coverage of the book -- you can look at the Contents. What follows the Contents in the book is the list of exercises -- if you remember what it is that you want to find by name (Schur's inequality... 3x3 block inverse... determinant of the bordered Gramian...) you might be able to do that from that list. So the second use of the book beside the obvious source of homework, practice and test problems is a reference on the interesting results in matrix theory -- and not just the plain vanilla matrix algebra as one probably had had in their undergraduate courses (linear spaces, bases, ranks, linear systems, determinants, inverses -- and there's relatively not that much of it, as other books will have that covered in greater detail), but with all the stuff that one would need for serious multivariate research -- matrix calculus, vectorizations and Kronecker products, factorizations, commutation and duplication matrices. It was a savior for my research work time with those advanced results a couple of times.

Highly recommended for:
* any teacher of a graduate level course that involves serious matrix operations (advanced linear models, advanced multivariate statistics; the authors come from econometric tradition, so there must be some advanced econometric classes where that would be an important book, although I would probably see this stuff scattered over several courses, as far as I understand the typical econometric sequences);
* any researcher developing multivariate techniques that are heavily matrix-based. I work in structural equation modeling, and I've also found uses of matrix calculus in my earlier work in spatial statistics, although mostly based on earlier Jan Magnus' book with Heinz Neudecker, Matrix Calculus, that I was translating to Russian at some point in my life. Another suggested book specifically for multivariate results in matrix forms, in the most abstract ways, is Kollo and von Rosen, Advanced Multivariate Statistics with Matrices.

I think this book is a good reference book for the matrix tools used in econometrics.