Phillips, Peter C. B. The exact distribution of LIML. I. (English) Zbl 0659.62059 Int. Econ. Rev. 25, 249-261 (1984). 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. Cited in 1 ReviewCited in 18 Documents MSC: 62H10 Multivariate distribution of statistics 62E15 Exact distribution theory in statistics 62P20 Applications of statistics to economics Keywords:limited information maximum likelihood (LIML) estimator; known error covariance matrix; simultaneous equations econometric model; multivariate Cauchy distribution; smallest latent roots; central Wishart matrix; matrix ratio of two independent Wishart matrices PDFBibTeX XMLCite \textit{P. C. B. Phillips}, Int. Econ. Rev. 25, 249--261 (1984; Zbl 0659.62059) Full Text: DOI Link