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Noncentral Student distributed LS and IV Estimators

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  • Leon Wegge

Abstract

The distribution of the least squares and the instrumental variable estimators of the coefficients in a linear relation is noncentral student when the data are normally distributed around possibly non-constant means. This is the claim of the paper and we show for what definition of a noncentral student density this claim to compact summary of the vast literature is justified. Unfortunately, the definition of the noncentral student density is as complicated as its parent, the noncentral Wishart density. Both are defined in terms of infinite series of zonal polynomials of all orders. We have developed however a recursive online method that generates these polynomials sequentially ad infinitum for bivariate and trivariate densities. The time is here that the practicality of the theory can be widened considerably.

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  • Leon Wegge, "undated". "Noncentral Student distributed LS and IV Estimators," Department of Economics 00-07, California Davis - Department of Economics.
    • Handle: RePEc:fth:caldec:00-07
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    File URL: http://www.econ.ucdavis.edu/working_papers/00-7.pdf
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    References listed on IDEAS

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    1. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    2. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
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