Prediction in Orlicz Spaces
In this paper, we investigate the prediction (or best approximation) operator from a uniformly convex real Orlicz space to a subset of σ-lattice measurable functions. In particular, a counterexample to the monotoncity property, which holds in Lp spaces, is given. Also, a sufficient condition for monotonicity to hold is given. Finally, nested σ-lattices, as occur in isotonic regression, are considered.
R B. Darst, David A. Legg, and Douglas W. Townsend (1981).
Prediction in Orlicz Spaces. Manuscripta Mathematica.35 (1), 91-103.