Stute, Winfried Bootstrap of linear model with AR-error structure. (English) Zbl 0838.62051 Metrika 42, No. 6, 395-410 (1995). Summary: We consider a linear model with autoregressive error structure. It is shown that with probability one the distribution of the two-stage GLS estimator admits a bootstrap approximation. In a simulation study it is demonstrated that the bootstrap outperforms the normal approximation if the innovation variables are heavily correlated. Cited in 5 Documents MSC: 62J05 Linear regression; mixed models 62G09 Nonparametric statistical resampling methods 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62E20 Asymptotic distribution theory in statistics Keywords:generalized least squares; linear model; autoregressive error structure; two-stage GLS estimator; bootstrap approximation; simulation study; normal approximation PDFBibTeX XMLCite \textit{W. Stute}, Metrika 42, No. 6, 395--410 (1995; Zbl 0838.62051) Full Text: DOI EuDML References: [1] Amemiya T (1973) Generalized least squares with an estimated autocovariance matrix. Econometrica 41: 723–732 · Zbl 0305.62046 · doi:10.2307/1914092 [2] Amemiya T (1989) Advanced econometrics. Oxford, Blackwell · Zbl 0698.62003 [3] Bickel PJ, Freedman DA (1981) Some asymptotic theory of the bootstrap. Ann Statistics 9:1196–1217 · Zbl 0472.62054 · doi:10.1214/aos/1176345637 [4] Freedman DA (1981) Bootstrapping regression models. Ann Statistics 9:1218–1228 · Zbl 0472.62071 · doi:10.1214/aos/1176345638 [5] Freedman DA (1984) On bootstrapping two-stage least-squares estimates in stationary linear models. Ann Statistics 12:827–842 · Zbl 0542.62051 · doi:10.1214/aos/1176346705 [6] Jing CG, Lai TL, Wei CZ (1981) Convergence systems and strong consistency of least squares estimates in regression models. J Multiv Analysis 11:319–333 · Zbl 0471.62065 · doi:10.1016/0047-259X(81)90078-6 [7] Judge GG, Hill RC, Griffiths WE, Luetkepohl H, Lee TC (1988) Introduction to the theory and practice of econometrics. New York Wiley [8] Solo V (1981) Strong consistency of least squared estimators in regression with correlated disturbances. Ann Statistics 9:689–693 · Zbl 0477.62048 · doi:10.1214/aos/1176345476 [9] Stout WF (1974) Almost sure convergence New York Academic Press · Zbl 0321.60022 [10] Wickens MR (1969) The consistency and efficiency of generalized least squares in simultaneous equation systems with autocorrelated errors. Econometrica 37:651–659 · Zbl 0184.42903 · doi:10.2307/1910440 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.