# UMBR

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 {it Z. Geng} and {it N.-Z. Shi}’s algorithm AS 257 [J. R. Stat. Soc., Ser. C 39, No. 3, 397--402 (1990; Zbl 0715.62055)], which only considered the one-dimensional case; and they also generalize {it G. Bril} et al.’s algorithm AS 206 [“Algorithm AS 206. Isotonic regression in two independent variables”, ibid. 33, No. 3, 352--357 (1984; url{doi:10.2307/2347723})], 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.

## References in zbMATH (referenced in 1 article , 1 standard article )

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