tailieunhanh - Handbook of Econometrics Vols1-5 _ Chapter 37

Chapter 37EMPIRICAL PROCESS IN ECONOMETRICS METHODS This paper provides an introduction to the use of empirical process methods in econometrics. These methods can be used to establish the large sample properties of econometric estimators and test statistics. In the first part of the paper\ | Chapter 37 EMPIRICAL PROCESS METHODS IN ECONOMETRICS DONALD . ANDREWS1 Cowles Foundation Yale University Contents Abstract 2248 1. Introduction 2248 2. Weak convergence and stochastic equicontinuity 2249 3. Applications 2253 . Review of applications 2253 . Parametric Af-estimators based on non-differentiable criterion functions 2255 . Tests when a nuisance parameter is present only under the alternative 2259 . Semiparametric estimation 2263 4. Stochastic equicontinuity via symmetrization 2267 . Primitive conditions for stochastic equicontinuity 2267 . Examples 2273 5. Stochastic equicontinuity via bracketing 2276 6. Conclusion 2283 Appendix 2284 References 2292 This paper is a substantial revision of the first part of the paper Andrews 1989 . I thank D. McFadden for comments and suggestions concerning this revision. I gratefully acknowledge research support from the Alfred P. Sloan Foundation and the National Science Foundation through a Research Fellowship and grant nos. SES-8618617 SES-8821021 and SES-9121914 respectively. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved 2248 . Andrews Abstract This paper provides an introduction to the use of empirical process methods in econometrics. These methods can be used to establish the large sample properties of econometric estimators and test statistics. In the first part of the paper key terminology and results are introduced and discussed heuristically. Applications in the econometrics literature are briefly reviewed. A select set of three classes of applications is discussed in more detail. The second part of the paper shows how one can verify a key property called stochastic equicontinuity. The paper takes several stochastic equicontinuity results from the probability literature which rely on entropy conditions of one sort or another and provides primitive sufficient conditions under which the entropy conditions hold. .