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is the asymptotic standard error of equation (1) defined as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] being a consistent estimator of the asymptotic variance of [?
1] is no longer a consistent estimator for b, but [[?
The purposes of this study are to: (1) Develop an analytic form for a weighting function that can be used to estimate weighted means that consistently estimate the population mean from incomplete data when covariates are measured with error; (2) Develop a consistent estimator of the weighting function and the population mean when covariates are measured with error; and (3) Evaluate the small sample properties of the estimator through a simulation study.
T] is allowed to be a fixed matrix that does not depend on the data and [theta] (identity matrix, for example), a matrix that depends on the data but not on [theta], or a matrix that depends on the data and a preliminary consistent estimator of [[theta].
is b without its first component, and gives a consistent estimator of [[OMEGA].
Nevertheless, a consistent estimator of [alpha] is available from the first-stage probit estimation of the selection equation:

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