# [R-sig-eco] MLEs for wrapped Cauchy

Dixon, Philip M [STAT] pdixon at iastate.edu
Sat Sep 24 15:48:31 CEST 2011

Lene,

The problem could be a bad starting value, optim wandering into places it shouldn't, insufficient data to estimate c, or something else.

A good way to understand what's going on is to plot profile likelihood against values of c.  For a specified value of c, use optim() to find the 2 parameter mle of  (mu0, rho0) given c.  Evaluating lnl at (\hat mu0, \hat rho0, c) gives you profile lnl(c) = max lnl (over mu0, rho0 given c).  Do that for a range of c and plot profile lnl(c) against c.

If optim() refuses to work well with the three parameter problem, you can always use optimize() on the profile likelihood.  Golden section search (in optimize) for a 1 parameter optimization is more numerically robust than conjugate gradient optimization.

Philip Dixon