tailieunhanh - Handbook of Econometrics Vols1-5 _ Chapter 39

Abstract A brief account is given of the methodology and theory for the bootstrap. Methodology is developed in the context of the “equation” approach, which allows attention to be focussed on specific criteria for excellence, such as coverage error of a confidence interval or expected value of a bias-corrected estimator. | Chapter 39 METHODOLOGY AND THEORY FOR THE BOOTSTRAP PETER HALL1 Australian National University Contents Abstract 2342 1. Introduction 2342 2. A formal definition of the bootstrap principle 2345 3. Iterating the principle 2352 4. Asymptotic theory 2357 . Summary 2357 . Edgeworth and Cornish-Fisher expansions 2358 . Edgeworth and Cornish-Fisher expansions of bootstrap distributions 2362 . Different versions of bootstrap confidence intervals 2364 . Order of correctness of bootstrap approximations to critical points 2367 . Coverage error of confidence intervals 2369 . Simple linear regression 2375 References 2379 Australian National University Canberra and CSIRO Division of Mathematics and Statistics Sydney Australia. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved 2342 P. Hall Abstract A brief account is given of the methodology and theory for the bootstrap. Methodology is developed in the context of the equation approach which allows attention to be focussed on specific criteria for excellence such as coverage error of a confidence interval or expected value of a bias-corrected estimator. This approach utilizes a definition of the bootstrap in which the key component is replacing a true distribution function by its empirical estimator. Our theory is Edgeworth expansion based and is aimed specifically at elucidating properties of different methods for constructing bootstrap confidence intervals in a variety of settings. The reader interested in more detail than can be provided here is referred to the recent monograph of Hall 1992 . 1. Introduction A broad interpretation of bootstrap methods argues that they are defined by replacing an unknown distribution function F by its empirical estimator F in a functional form for an unknown quantity of interest. From this standpoint the individual who first suggested that a population mean H x dF x could be estimated by the sample mean