Practical Genetic Algorithms
thor is presented in a simple situation at the beginning of Chapter 2 [formulas (2.5) and (2.11)]. This provides a unified way to carry out computations. The following chapters are devoted to particular models: standard least squares regression (Chap. 4), models with heteroscedasticity and correlation and SURE and panel data models (Chap. 5), time series models (Chap. 6), and simultaneous equations models (Chap. 7). An appendix collecting many useful basic results is provided at the end of the book. The book has two major strengths. First, it presents finite-sample results in a unified way, and it can be used as a basic reference by graduate students and researchers in econometrics and statistics. Second, it covers important econometric models by providing finite-sample results where these are available. From these points of view, this book is unique. What is missing? One could argue that a good transparent approximation based on asymptotic theory might sometimes be preferable to a complex exact finite-sample result. This is typically the case with saddlepoint approximations (Daniels 1954; Field and Ronchetti 1990), which are mentioned only briefly. There has been significant research in this field in the past 20 years, and these techniques can now be applied beyond the original simple case of the mean. In fact, very accurate approximations are available in general setups, including, for instance, multivariate M-estimators (see the references in Ronchetti 1997). Related to this and missing is the nice exact formula for the density of a maximum likelihood estimator in a general parametric model (see Skovgaard 1990; Hillier and Armstrong 1999). From the point of view of presentation, the book focuses on analytic results, and numerical results and computational aspects are scarce. This book is a good reference on exact finite-sample results in econometrics and is a valuable addition to any statistical library. It can be used as a text in a special graduate level course in econometrics and statistics. It would also be a useful reference for a researcher in these fields.