Center for Economic Research, Department of Economics, University of Minnesota
Based on the Pearson family of distributions, we have derived
some Lagrangean multiplier tests for the normality and homoscedasticity
assumptions in the censored regression models. The Lagrangean multiplier
test statistic for the joint test of selectivity bias, homoscedasticity
and normality is the sum of three components. Each component is
shown to be a conditional Lagrangean multiplier test statistic. It has
been shown that they can also be interpreted as tests of significance
of coefficients in some linear models based on instrumental variable
estimations. We have pointed out that for some very special cases, the
Lagrange multiplier tests for selectivity have had no power, and are not
equivalent, for large samples, to the likelihood ratio tests. This
situation occurs as the likelihood evaluated at the constrained MLE
is a stationary value of the unconstrained likelihood function. These
. examples provide, probably, the first set of examples to confirm a conjecture
in Silvey [1959, p. 399].
Lee, L., (1981), "A Specification Test for Normality in the Generalized Censored Regression Models", Discussion Paper No. 146, Center for Economic Research, Department of Economics, University of Minnesota.
A Specification Test for Normality in the Generalized Censored Regression Models.
Center for Economic Research, Department of Economics, University of Minnesota.
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