Abstract
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.
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This author supported by a grant from the Indiana University-Purdue University at Fort Wayne Research and Instructional Development Support Program
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Darst, R.B., Legg, D.A. & Townsend, D.W. Prediction in Orlicz spaces. Manuscripta Math 35, 91–103 (1981). https://doi.org/10.1007/BF01168450
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DOI: https://doi.org/10.1007/BF01168450