Weighted empirical processes in dynamic nonlinear models. 2nd ed.

*(English)*Zbl 1007.62047
Lecture Notes in Statistics. 166. New York, NY: Springer. xvii, 425 p. (2002).

This book presents a unified approach for obtaining the limiting distributions of minimum distance, \(M\) and \(R\) estimators corresponding to non-smooth underlying scores in a large class of dynamic nonlinear models. It has also a discussion on classes of goodness-of-fit tests for fitting an error distribution in some of these models and fitting a regression-autoregression function in the absence of the knowledge of the error distribution. The main technique consists in the study of corresponding weighted residual empirical processes.

This book is an updated edition of the author’s earlier monograph, “Weighted empiricals and linear models”. (1992; Zbl 0998.62501). It includes material on asymptotically distribution free tests for fitting regression and autoregression models, the asymptotic distributions of autoregression quantiles and rank scores and the weak convergence of residual empirical processes useful in nonlinear ARCH models.

The author has contributed extensively to the area of weighted empirical processes and the monograph is well written. The book is a welcome addtion containing advances in the development of the asymptotic theory of robust inference procedures corresponding to non-smooth score functions from linear models for nonlinear dynamic models.

This book is an updated edition of the author’s earlier monograph, “Weighted empiricals and linear models”. (1992; Zbl 0998.62501). It includes material on asymptotically distribution free tests for fitting regression and autoregression models, the asymptotic distributions of autoregression quantiles and rank scores and the weak convergence of residual empirical processes useful in nonlinear ARCH models.

The author has contributed extensively to the area of weighted empirical processes and the monograph is well written. The book is a welcome addtion containing advances in the development of the asymptotic theory of robust inference procedures corresponding to non-smooth score functions from linear models for nonlinear dynamic models.

Reviewer: B.L.S.Prakasa Rao (New Delhi)