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Confidence Limits by Inversion


CML computes a covariance matrix of the parameters that is an approximate estimate when there are constrained parameters in the model (Gallant, 1987, Wolfgang and Hartwig, 1995). When the model includes inequality constraints, however, confidence limits computed from the usual t-statistics - dividing the parameter estimates by their standard errors - are incorrect because they do not account for boundaries placed on the distributions of the parameters by the inequality constraints.

For this reason, confidence limits must be calculated directly when the model contains constrained parameters. Two methods for such calculation are discussed here, by inversion of an appropriate statistic, and by simulation of the distribution of the parameter.

For further discussion of confidence limits by inversion of the likelihood ratio statistic see Cox (1974), Cook and Weisberg (1990), Meeker and Escobar (1995), Schoenberg (1997).

R. Schoenberg
Fri Sep 12 09:47:41 PDT 1997