Exploring Multivariate Data With the Forward Search

and other variables on electricity demand, where the nonparametric effect of weather is modeled additively. Finally, endogeneity of parametric or nonparametric variables in partial linear models is studied, and the asymptotic distribution of two-stage-least-squares differencing estimators is derived. Proofs of many results in Chapter 4 are collected in Appendix B, whereas Appendix C addresses the optimal choice of differencing weights. Chapter 5 focuses on nonparametric estimation of functions of several variables. In a first step, the convergence rate of multivariate kernel estimators is discussed, and the computation of two-dimensional nonparametric least squares estimators is explained. Additive models are then considered and the backfitting algorithm is presented. A variable ordering rule to apply consistent differencing estimators in a bivariate nonparametric setting is also proposed. Examples related to housing prices and household gasoline demand are discussed. Chapter 6 is devoted to nonparametric constrained estimation and hypothesis testing. Kernel-based algorithms for estimating monotone regression functions are briefly presented. Nonparametric least squares is shown to be a useful method to incorporate monotonicity, concavity, and other restrictions. The methods are applied to estimation for simulated option prices under monotonicity and convexity constraints. Different forms of asymptotic goodness-of-fit tests, residual regression tests, specification tests, and significance tests are explained in the first part of the chapter, together with implementation details for applied purposes. Appendix D contains a more formal description of nonparametric least squares methods. Chapter 7 studies index models and related semiparametric specifications in more depth. Grid search estimation procedures for index models are explained. Parameter identification is briefly discussed, and the relevant estimator’s asymptotic distribution is given. In a real-data application to Engel curves, a flexible index model for equivalence scales of any pair of family types is estimated. Estimation of partial linear models including an index component is then introduced, together with two applications estimating and testing base-independent equivalence scales. Chapter 8 introduces bootstrap procedures. After an intuitive introduction, a nontechnical discussion of bootstrap validity is given, and reasons for bootstrap failure are highlighted. The wild bootstrap is included as a useful alternative for heteroscedastic settings. Implementation details are provided for bootstrapping confidence intervals for kernel smoothers, nonparametric goodness-of-fit and residual regression tests, and parameter estimates of partial linear and index models. Appendix A contains standard mathematical preliminaries and basic notation. Besides advocating the use of differencing procedures as simple methods for nonparametric and semiparametric regression analysis, the author applies nonparametric least squares methods to take general nonparametric constraints into account. In a future edition, it might be interesting to consider enlarging the very useful chapter on the bootstrap by studying applied examples where the bootstrap might fail but subsampling procedures apply; see Politis, Romano, and Wolf (1999) for a review of subsampling methods. In contrast to, for instance, Pagan and Ullah (1999), the book covers material and applications that are confined to settings with independent observations: with the exception of residual correlation, time-dependent data issues are not covered. An important microeconometric topic not addressed is the seminonparametric estimation of discrete choice, selectivity, and censored regression models; these topics are for instance treated in Horowitz (1998) or Pagan and Ullah (1999). Given the microeconometric focus of the book, an inclusion of such examples would have been useful.