Asymptotic number of roots of Cauchy location likelihood equations.

The current research addresses one particular case, of interest more to the theory of robust estimation than to any particular problem in applied statistics. This is the problem of estimating the center of the distribution of independently identically distributed Cauchy random variables. Although there could theoretically be as many local maxima to the likelihood function as there are observations, the number of local maxima that occur in practice is actually quite small.