"A collection of proofs of fundamental theorems, this volume utilizes a format that is exhaustive and consistent. Every result covered in ``Econometrics''is proved as well as stated. One notation system is used throughout the volume. The topics included in the book cover such areas as estimations and testing in linear regression models under various sets of assumptions, and estimation and testing in simultaneous equations models. The latter subject is treated more extensively than in most econometrics books, and the entire volume is characterized by its rigorous level of examination. "
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2SLS estimator 3SLS asymptotic covariance matrix asymptotic distribution asymptotically efficient coefficient consider consistent estimator constant term converges in distribution COROLLARY defined degrees of freedom dimension disturbances Econometric efficient relative elements exactly identified exists FIML estimator finite and nonsingular full column rank full ideal conditions Hence idempotent identical implies independent indirect least squares instrumental variables k-class estimator least squares estimator Lemma likelihood function linear combination LVR estimator maximize maximum likelihood estimator minimizing nonsingular matrix nonstochastic normal distribution normal equations notation Note null hypothesis observations OLS estimator overidentified partition plim positive semidefinite priori restrictions probability limit Proof PROPOSITION random variables regressors satisfies the full scalar Section 1.5 seemingly unrelated regressions sequence set of equations solution squared errors submatrix sufficient condition sum of squared test statistic Theorem trace unbiased estimator variance vector zero mean