| The subject of this book is estimating parameters of expectation models of statistical observations. The book describes what I consider the most important aspects of the subject for applied scientists and engineers. From experience, I know that this group of users is often not aware of estimators other than least squares. Therefore, one of my purposes is to show that statistical parameter estimation has much more to offer than least squares estimation alone. To resort to least squares estimation almost automatically is, in fact, a purely expectation model oriented approach since the statistical properties of the observations are disregarded. In the approach of this book, knowledge of the distribution of the observations is involved in the choice of estimator. I hope to show that thus the available a priori knowledge may be used more fully to improve the precision of the estimator. A further advantage of the chosen approach is that it unifies the underlying theory and reduces it to a relatively small collection of coherent, generally applicable principles and notions. Moreover, this offers the opportunity to teach the subject in a systematic way.
The book is intended for a broad category of users: applied scientists, engineers, and undergraduate and graduate students. To enhance its suitability as course material and for exercise in general, I have included Problems in Chapters 3-6. Throughout, I have assumed that users have an elementary knowledge of statistics. They should be familiar with notions such as univariate and multivariate distribution, expectation, covariance, and hypothesis testing. In this respect, references such as [25, 20, 241 might be helpful. |
