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The exact distribution of LIML. I. (English) Zbl 0659.62059

The author derives exact probability density functions of (i) the limited information maximum likelihood (LIML) estimator and (ii) the LIMLK estimator (the LIML estimator utilizing a known error covariance matrix) of the common single equation coefficient vector in the simultaneous equations econometric model. These are given in the form of a multivariate Cauchy distribution in the leading case when \(\Pi_{22}=0\) is assumed in the reduced form of the model. The two estimators are given as ratios of components of the latent vectors corresponding to the smallest latent roots of a central Wishart matrix and a matrix ratio of two independent Wishart matrices, respectively. Some multivariate statistical methods are utilized in the derivation.

MSC:

62H10 Multivariate distribution of statistics
62E15 Exact distribution theory in statistics
62P20 Applications of statistics to economics
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