A Note on Estimation in Seemingly Unrelated Semi-Parametric Regression Models
In this paper a system of two seemingly unrelated semi-parametric regression models is considered, in which, following the partial residual procedure, we first show that the weighted least squares estimator (WLSE) of the regression parameter from the system can be expressed as a matrix series. Then this estimator is shown to be the limit of the covariance-adjusted estimator sequence of the regression parameter. Furthermore, based on the matrix series, we prove that the WLSE actually has only one unique simpler form, which exactly equals to the one-step covariance-adjusted estimator of the regression parameter. We also show that when the variance-covariance matrix of disturbances is unknown, the corresponding two-stage WLSE too has exactly one simpler form, and for any finite k ≥ 2, the k-step covariance-adjusted estimator degenerates to the one-step covariance-adjusted estimator. Finally, we generalize our above conclusions to the system of m(m ≥ 3) seemingly unrelated semi-parametric regressions and point out that the conclusions presented in this paper include the system of m(m ≥ 2) seemingly unrelated linear regressions as its special case.
Volume (Year): 10 (2012)
Issue (Month): 1 (January)
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- Raymond J. Carroll & Douglas Midthune & Laurence S. Freedman & Victor Kipnis, 2006. "Seemingly Unrelated Measurement Error Models, with Application to Nutritional Epidemiology," Biometrics, The International Biometric Society, vol. 62(1), pages 75-84, 03.
- Swamy, P. A. V. B. & Mehta, J. S., 1975. "On Bayesian estimation of seemingly unrelated regressions when some observations are missing," Journal of Econometrics, Elsevier, vol. 3(2), pages 157-169, May.
- Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
- Schmidt, Peter, 1977. "Estimation of seemingly unrelated regressions with unequal numbers of observations," Journal of Econometrics, Elsevier, vol. 5(3), pages 365-377, May.
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