This text covers regression techniques which the author views as the most commonly used statistical technique especially in the world of insurance and finance. Since the book is in a series for actuarial science I expected the presentation to be elementary to intermediate and to only cover regression. However, at times the topics get pretty advanced. Theorems are presented but not with proofs.
In my mind survival analysis which is extremely important to actuaries and time series analysis which in very important to finance would not be covered as they do not fall into the category of regression. But thankfully they are included.
Some time series models such as polynomial functions of time can be viewed as linear regression models where time is the predictor variable for the response. These are special cases of trend models. But the main models like exponential smoothing, Box-Jenkins and ARCH/GARCH which are the main ones applied in financial forecasting are really not regression in my view. But these too are covered in the book.
The book starts out in Chapter 1 with a very elementary review of statistics and simple forms of regression. Then Chapter 2-6 form part I which is titled Regression. Chapter 2 presents the basics of simple linear regression. Chapters 3 and 4 cover multiple regression. This is not a cookbook of techniques. The author provides background, historical developments and important concepts and mixes in applications to actuarial science and finance throughout. At the end of most chapters are a large number of exercises with solutions for selected problems in the back.
In chapter 3 the author explains least squares presents the modeling assumptions and introduces the Gauss-Markov theorem as well as all the standard concepts of hypothesis testing that a regression parameter is significant, R-square and theorem (hence also the concept of minimum variance among unbiased estimators). In Chapter 4 he provides the unified theme of the general linear hypothesis as he covers categorical predictor variables, the analysis of variance and covariance (all general linear models) In Chapter 5 leverage points and influential points, multicollinearity, and regression diagnostics are presented in the context of variable selection. Chapter 6 is all about interpretation and limitations.
Later in parts III and IV the author introduces nonlinear regression models, logistic regression, probit and tobit models, Poisson and negative binomial regression, generalized linear models, and specialized techniques such as bootstrapping, mixed linear models, proportional hazards regression, generalized additive models and the Bayesian approach to regression. The coverage gets more advanced as you move through the chapters. Part II on time series includes seasonal models, discussion of stationary and longitudinal and panel data models. In Part III survival analysis is included in Chapter 14. This includes the Kaplan-Meier estimates, proportional hazards regression, accelerated failure time models and even the analysis of recurrent events.
Part IV specifically focuses on actuarial applications and it is here that heavytailed distributions are dealt with using quantile regression and extreme value probability models. It also includes advice on presentation with Chapter 20 covering report writing and Chapter 21 on designing effective graphs. Chapters 18 and 19 respectively covering credibility and claims or loss triangles are very specific to actuarial science.
With such an extensive list of topics the book is a large volume of over 560 pages. But even so it is not possible to do justice to this extensive list. The author provides an outstanding list of references at the end of the chapters that provides additional reading on the various topics. In addition the author provides programs in SAS and R as well as output form these packages. More detailed examples and projects can be found in the books.