Starr Global Optimality Test {accuracy}R Documentation

Function to test that an optimum from MLE, NLS, or other non-linear optization routine is a global optimum

Description

Implements the Starr test for identification of the global optimum of a likelihood surface.

Usage

 starr(betas, tol=.0001, dmethod="euclidean")

Arguments

betas Vector of parameter values
tol Tolerance distance between two parameter vectors to consider as "unique" optimum
dmethod method used to compute distance between two parameter vectors

Details

texttt{starr} computes the probability that a local optimum, which may or may not be the global optimum, of a likelihood function has not been observed. The probability is generated by counting the observed number of ``basins of attraction'' - starting values that lead to an local optimum.

Value

texttt{starr} is a class "double" with value equal to the probability than a local optimum is unobserved.

Note

texttt{starr} is given a vector of texttt{betas} parameter values identifying local optima resultant of a search algorithm, such as texttt{mle} or texttt{nls}. The starting values used to generate texttt{betas} can be a grid, or for larger n-dimenional parameter spaces, may be randomly chosen. The parameter values identifying a local optimum are passed to texttt{starr} for each set of starting values that lead to that local optimum.

Author(s)

Micah Altman Micah_Altman@harvard.edu http://www.hmdc.harvard.edu/micah_altman/ , Michael McDonald

References

Altman, M., J. Gill and M. P. McDonald. 2003. Numerical Issues in Statistical Computing for the Social Scientist. John Wiley & Sons. http://www.hmdc.harvard.edu/numerical_issues/

Finch, S. J., Mendell, N. R., Thode, H. C., Jr. 1989. ``Probabilistic Measures of Adequacy of a Numerical Search for a Global Maximum.'' Journal of the American Statistical Association {bf 84}, 1020-3.

Starr, N. 1979. ``Linear Estimation of the Probability of Discovering a New Species.'' Annals of Statistics {bf 7}, 644-52.


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