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The distributions of deviations of point estimators for parameters of interest are essential in the evaluation of the efficiency of point estimators. The bootstrap method suggested by B. Efron is one of the main methods directed at solving the problem of producing distributions which mimic the unobserved distributions of deviations. The main object of this article is to study the asymptotic validity of the bootstrap in the context of heteroscedastic regression models, using the central limit resampling theorem. In the case of one-parameter linear regression, theoretical results are illustrated by an example with simulated statistical data.
Czasopismo
Rocznik
Tom
Strony
265--276
Opis fizyczny
Bibliogr.14 poz.
Twórcy
autor
- 14 Academici st., Faculty of Mathematics Bucharest University, Romania, str. Eftimiu Mache, Nr. 25A Bucharest Sector 5, Romania
Bibliografia
- [1] P. Bickel and D. Freedman, Sow asymptotic theory for the bootstrap, Ann. Statist 9 (1981), pp. 1196-1217.
- [2] P. Bickel and D. Freedman, Bootstrapping Regression Models with Many Parameters. A Festschrift for Erich L. Lehman, Wadsworth, Belmont, C.A., 1983, pp, 28-48.
- [3] N. J. Delaney and S, Chatterjee, Use of the bootstrap and cross-validation in ridge regression, J. Business Economic Statist. 4 (1986), pp. 255-262.
- [4] B. Efron, Bootstrap methods: Another took at the jackknife, Ann, Statist 7 (1979), pp, 1 26.
- [5] B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans, Regional Conference Series in Applied Mathematics, Monograph 38, SIAM, Philadelphia 1982.
- [6] 8, Efron and R. J. Tibshirani, Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy, Statist Sci. 1 (1986), pp. 54-77.
- [7] D. Freedman, Bootstrapping regression models, Ann. Statist. 9 (1981), pp. 1218-1228.
- [8] D. Freedman, On two-stage least squares estimates in stationary linear models, Ann. Statist. 12 (1984), pp. 827-842.
- [9] D. Freedman and S. C. Peters, Bootstrapping an econometric model: some empirical results, J. Business Economic Statist 2 (1984), pp. 150-158.
- [10] P. Hall and E, Mammen, On general resampling algorithms and their performance in distribution estimation, Ann. Statist. 22 (1994), pp. 2011-2030.
- [11] S. Holm, Abstract bootstrap confidence intervals in linear models, Scand. J. Statist. 20 (1990), pp. 157-170.
- [12] W. Navidi, Edgeworth expansions for bootstrapping regression models, Ann. Statist., 17 (1989), pp. 1472-1478.
- [13] ML Stone and R. J, Brooks, Continuum regression: Cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal components regression, J. Roy. Statist. Soc. Ser. B 52 (1990), pp. 237-269.
- [14] C. F. J. W u, Jackknife, bootstrap and other resampling methods in regression analysis, Ann. Statist. 14 (1986), pp. 1261-1295.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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