Generalized continuous isotonic regression

The standard isotonic regression of a vector in RnRn is the solution to a least squares projection problem on the cone CC of vectors with ‘increasing components’ in RnRn. Generalized isotonic regression problems are isotonic optimization problems that seem to be quite different from isotonic regression problems, but in fact have the same solution. In problems of maximum smoothed likelihood estimation, often continuous versions of generalized isotonic regression problems emerge. In this paper we show that the solutions to such problems are often given by the relatively simple continuous isotonic regression of a function. We illustrate the result using the problem of maximum smoothed likelihood estimation of an increasing hazard function.