A note on approximating moments of least squares estimators

Liu-Evans, Gareth (2014): A note on approximating moments of least squares estimators.

Abstract

Results are presented for approximating the moments of least squares estimators, particularly those of the OLS estimator, and the methodology is illustrated using a simple dynamic model.

• Item Type: MPRA Paper
• Language: English
• Keywords: asymptotic approximation, bias, least squares, time series, simulteneity
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General

References

Bao, Y., 2007. The approximate moments of the least squares estimator for the stationary autoregressive model under a general error distribution. Econometric Theory 23(05), 1013–1021.

Bao, Y., Ullah, A., 2007. The second-order bias and mean-squared error of estimators in time-series models. Journal of Econometrics 140(2), 650–669.

Kendall, M., 1954. Note on bias in the estimation of autocorrelation. Biometrika 61, 403–404.

Kiviet, J., Phillips, G., 1994. Bias assessment and reduction in linear error-correction models. Journal of Econometrics 63, 215–243.

Kiviet, J., Phillips, G., 1996. The bias of the ordinary least squares estimator in simultaneous equation models. Economics Letters 53, 161–167.

Kiviet, J., Phillips, G., 2005. Moment approximation for least-squares estimators in dynamic regression models with a unit root. Econometrics Journal 8, 1–28.

Kiviet, J., Phillips, G., 2012. Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models. Computational Statistics and Data Analysis 56(11), 3706–3729.

Kiviet, J., Phillips, G., 2014. Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models. Computational Statistics and Data Analysis 76, 424–448.

Magnus, J., Neudecker, H., 1979. The commutation matrix: some properties and applications. The Annals of Statistics 7(2), 318–394.

Magnus, J., Neudecker, H., 2002. Matrix differential calculus with applications in statistics and econometrics (Revised edition). Wiley.

Marriott, F., Pope, J., 1954. Bias in the estimation of autocorrelations. Biometrika 61, 393–403. Nagar, A., 1959. The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations. Econometrica 27, 575–595.

Neudecker, H., 1969. Some theorems on matrix differentiation with special reference to kronecker matrix products. Journal of the American Statistical Association 64 (327), pp. 953–963.

Neudecker, H., Wansbeek, T., 1983. Some results on commutation matrices, with statistical applications. The Canadian Journal of Statistics / La Revue Canadienne de Statistique 11 (3), pp. 221–231.

Phillips, G., 2000. An alternative approach to obtaining nagar-type moment approximations in simultaneous equation models. Journal of Econometrics 97(2), 345–364.

Rilestone, P., Srivastava, S., Ullah, A., 1996. The second-order bias and mean squared error of nonlinear estimators. Journal of Econometrics 75, 369–395.

Sargan, J., 1974. The validity of nagar’s expansion for the moments of econometric estimators. Econometrica 42, 169–176.

Sargan, J., 1976. Econometric estimators and the Edgeworth expansion. Econometrica 44, 421–448.

Shao, J., 1988. On resampling methods for variance and bias estimation in linear models. Annals of Statistics 16, 986–1008.

Shao, J., Tu, D., 1995. The Jackknife and Bootstrap, 1st Edition. Springer-Verlag, 175th Avenue, New York.

Ullah, A., 2004. Finite Sample Econometrics. Oxford University Press.