Question

The limiting behavior of multiple roots of the likelihood equation

Answer 1

Answer:

This chapter discusses the limiting behavior of multiple roots of the likelihood equation. It describes Cauchy distribution and the bivariate normal distribution with known variances and unknown correlation. Ω is an open interval to avoid difficulties arising from the nonexistence of solutions of the likelihood equation (LEQ) that can occur when the true parameter value lies on the boundary of the parameter space. The chapter discusses some examples of K-L ordered families. In the case of the two-parameter Cauchy family, with both location and scale parameters, the LEQs have a unique solution for all n and almost all sample sequences, and this solution gives the absolute maximum of the likelihood function, that is, the maximum likelihood estimate.