The Bias of Bootstrapped Versus Conventional Standard Errors in the General Linear and SUR Models
- 1 June 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 8 (2) , 258-275
- https://doi.org/10.1017/s0266466600012792
Abstract
When estimating the seemingly unrelated regression (SUR) model in small samples, the bootstrap feasible generalized least-squares (FGLS) covariance estimator has been widely advocated as less biased than the conventional FGLS covariance estimator obtained by evaluating the asymptotic covariance matrix. Assuming multivariate normal errors and an unbiased estimator of the error covariance, Eaton proves that the conventional estimator is biased downward for a general SUR model. Ignoring termsO(T–2) for this model, we prove that the bootstrap estimator is also biased downward. However, from these results, the relative magnitude of these two biases is indeterminant in general. By ignoring termsO(T–2) for Zellner's two-equation, orthogonal regressor model with bivariate normal errors, we show that the bias of both estimators is downward and that the bootstrap estimator exhibits a smaller bias than the conventional estimator. Monte Carlo simulation results indicate that, in general, neither estimator uniformly dominates the other.Keywords
This publication has 28 references indexed in Scilit:
- Second Order and $L^p$-Comparisons between the Bootstrap and Empirical Edgeworth Expansion MethodologiesThe Annals of Statistics, 1989
- Better Bootstrap Confidence IntervalsJournal of the American Statistical Association, 1987
- Better Bootstrap Confidence IntervalsJournal of the American Statistical Association, 1987
- Jackknife, Bootstrap and Other Resampling Methods in Regression AnalysisThe Annals of Statistics, 1986
- Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical AccuracyStatistical Science, 1986
- Bootstrapping a Regression Equation: Some Empirical ResultsJournal of the American Statistical Association, 1984
- Use of Restricted Residuals in SUR Systems: Some Finite Sample ResultsJournal of the American Statistical Association, 1976
- Use of Restricted Residuals in SUR Systems: Some Finite Sample ResultsJournal of the American Statistical Association, 1976
- Estimators for Seemingly Unrelated Regression Equations: Some Exact Finite Sample ResultsJournal of the American Statistical Association, 1963
- An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation BiasJournal of the American Statistical Association, 1962