Hira L. Koul

Weighted Empirical Processes in Dynamic Nonlinear Models (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book presents a unified approach for obtaining the limiting distributions of minimum distance. It discusses classes of goodness-of-t tests for fitting an error distribution in some of these models and/or fitting a regression-autoregressive function without assuming the knowledge of the error distribution. The main tool is the asymptotic equi-continuity of certain basic weighted residual empirical processes in the uniform and L2 metrics.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 425
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461300557
• Artikelnr.: 43991606

Autorenporträt

Hira L. Koul is a professor of statistics at Michigan State University. He is a Fellow of the IMS and an Elected Member of the International Statistical Institute. He was awarded the presti- gious Humboldt Research Award for Senior Researchers in 1995. He has been on the editorial boards of the Annals of Statistics, Sankhya, and J. Indian Statistical Association. Currently he is a Coordinating Editor of the Journal of Statistical Planning and Inference, and an Associate Editor of Statistics and Probability Letters.

Inhaltsangabe

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.'s.- 2.1 Introduction.- 2.2 Weak Convergence.- 2.3 AUL of Residual W.E.P.'s.- 2.4 Some Additional Results for W.E.P.'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.'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.