Author	Koul, Hira L. author
Title	Weighted Empirical Processes in Dynamic Nonlinear Models [electronic resource] / by Hira L. Koul
Imprint	New York, NY : Springer New York : Imprint: Springer, 2002
Edition	Second Edition
Connect to	http://dx.doi.org/10.1007/978-1-4613-0055-7
Descript	XVII, 425 p. 1 illus. online resource

The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an exยญ panded version of the monograph Weighted Empiricals and Linear Models, IMS Lecture Notes-Monograph, 21 published in 1992, that includes some aspects of this development. The new inclusions are as follows. Theorems 2. 2. 4 and 2. 2. 5 give an extension of the Theorem 2. 2. 3 (old Theorem 2. 2b. 1) to the unbounded random weights case. These results are found useful in Chapters 7 and 8 when dealing with hoยญ moscedastic and conditionally heteroscedastic autoregressive models, actively researched family of dynamic models in time series analysis in the 1990's. The weak convergence results pertaining to the partial sum process given in Theorems 2. 2. 6 . and 2. 2. 7 are found useful in fitting a parametric autoregressive model as is expounded in Section 7. 7 in some detail. Section 6. 6 discusses the related problem of fitยญ ting a regression model, using a certain partial sum process. Inboth sections a certain transform of the underlying process is shown to provide asymptotically distribution free tests. Other important changes are as follows. Theorem 7. 3

1 Introduction -- 1.1 Weighted Empirical Processes -- 1.2 M-, R- and Scale Estimators -- 1.3 M.D. Estimators & Goodness-of-fit Tests -- 1.4 R.W.E. Processes and Dynamic Models -- 2 Asymptotic Properties of W.E.P.โ{128}{153}s -- 2.1 Introduction -- 2.2 Weak Convergence -- 2.3 AUL of Residual W.E.P.โ{128}{153}s -- 2.4 Some Additional Results for W.E.P.โ{128}{153}S -- 3 Linear Rank and Signed Rank Statistics 69 -- 3.1 Introduction -- 3.2 AUL of Lin ear Rank Statistics -- 3.3 AUL of Linear Signed Rank Statistics -- 3.4 Weak Convergence of Rank and Signed Rank W.E.P.โ{128}{153}s -- 4 M, R and Some Scale Estimators -- 4.1 Introduction -- 4.2 M-Estimators -- 4.3 Distributions of Some Scale Estimators -- 4.4 R-Estimators -- 4.5 Est imation of Q(f) -- 5 Minimum Distance Estimators -- 5.1 Introduction -- 5.2 Definitions of M.D. Estimators -- 5.3 Finite Sample Properties -- 5.4 A General M.D. Estimator -- 5.5 Asymptotic Uniform Quadraticity -- 5.6 Distributions, Efficiency & Robustness -- 6 Goodness-of-fit Tests in Regression -- 6.1 Introducti on -- 6.2 The Supremum Distance Tests -- 6.3 L2-Distance Tests -- 6.4 Testing with Unknown Scale -- 6.5 Testing for the Symmetry of the Errors -- 6.6 Regression Model Fitting -- 7 Autoregression -- 7.1 Introduction -- 7.2 AUL of Wh and Fn -- 7.3 GM- and GR- Estimators -- 7.4 Minimum Distance Estimation -- 7.5 Autoregression Quantiles and Rank Scores -- 7.6 Goodness-of-fit Testing for F -- 7.7 Autoregressive Model Fitting -- 8 Nonlinear Autoregression 358 -- 8.1 Introduction -- 8.2 AR Models -- 8.3 ARCH Models -- Lectures Notes in Statistics