ISOTONIC REGRESSION IN TWO INDEPENDENT VARIABLES UNDER UMBRELLA ORDERINGS

This paper proposes two FORTRAN algorithms, namely UMBR and UUMBR, for computing isotonic regression in two independent variables under an umbrella order for the peak of the umbrella being known and unknown respectively. They extend Geng and Shi (1990)'s algorithm AS 257, which only considered the one-dimensional case; and they also generalize Bril et al. (1984)'s algorithm AS 206, which only studied the two-dimensional simple order. The two algorithms presented here can be also used to compute the maximum likelihood estimator of normal means under two-dimensional umbrella order restrictions.