dehaan {accuracy} | R Documentation

## dehaan global optimality test

### Description

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

### Usage

       dehaan(llTest, llMax, pval=.05 )

### Arguments

`llTest` | Vector of randomly generated likelihood values
`llMax` | Value of the likelihood function for a candidate global optimum
`pval` | p-value of the test

### Details

dehaan computes a (1-p) confidence interval for the global optimum of a likelihood surface from a vector of user-supplied randomly chosen likelihood values. A user-supplied candidate maximum likelihood value is evaluated against confidence interval.

### Value

dehaan=TRUE if the candidate value is greater than the (1-p) confidence interval for the true optimum.

### Note

The choice of the vector of user-supplied random likelihood values is somewhat of an art. The parameter space should be large enough to capture the true optimum, but not so large as to include illegal or impractical parameter values.

The generated confidence interval depends on the number of random draws from the parameter space. The number should be large enough to allow the application of asympotic theory. A recommended number of random evaluations of the likelihood function at a given set of parameter values is 500 or more, but depends on the size of the parameter space. Users are encouraged to experiment with more and less draws and observe results.

### Author(s)

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

de Haan, L. 1981. ``Estimation of the Minimum of a Function Using Order Statistics.'' Journal of the American Statistical Association 76, 467-9.

Veall, M. R. 1990. ``Testing for a Global Maximum in an Econometric Context.'' Econometrica 58 1459-65.

### Examples

      # The deHaan test is constructed as a maximum likelihood
      # test, with negative values for the likelihood.  The BOD problem
      # is a non-linear least squares minimization problem.  This test
      # is implemented using the negative of the sum of squares for consistency
      # with the deHaan framework of maximum likelihood.

      BOD <-
    structure(list(Time = c(1, 2, 3, 4, 5, 7), demand = c(8.3, 10.3,
    19, 16, 15.6, 19.8)), .Names = c("Time", "demand"), row.names = c("1",
    "2", "3", "4", "5", "6"), class = "data.frame", reference = "A1.4, p. 270")
      stval<-expand.grid(A = seq(10, 100, 10), lrc = seq(.5, .8, .1))
      llfun<-function(A,lrc,BOD)
            -sum((BOD$demand - A*(1-exp(-exp(lrc)*BOD$Time)))^2)
      lls<-NULL
      for (i in 1:nrow(stval))  {
         lls = rbind(lls, llfun(stval[i,1], stval[i,2],BOD))
      }
      fm1 <- nls(demand ~ A*(1-exp(-exp(lrc)*Time)),
                    data = BOD, start = c(A = 20, lrc = log(.35)))
      ss = -sum(resid(fm1)^2)
      dehaan(lls, ss)

[Package accuracy version 1.35 Index]