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Statistical Inference in Constrained Models

An implementation and evaluation is presented of Andrews (1999) method for statistical inference for models with restricted parameters. This method produces confidence limits by encapsulating the distorted acceptance region with a regular hyper-ellipsoid and simulating a distribution of the parameters within it.

From 1969 when quasi-Newton methods were first implemented for maximum likelihood estimation restricted parameter spaces presented difficulties for both the optimization and statistical inference. Nonlinear programming methods introduce in the 90's solved the optimization problem and now the Andrews method purports to solve the inference problem.

The presentation will include an overview of optimization and maximum likelihood methods from 1969 through the present time and will conclude with results of simulations of the different methods commonly used for statistical inference in addition to the Andrews method.

Andrews, D.W.K., 1999. "Estimation when a parameter is on a boundary", Econometrica_, 67:1341-1383.