In this paper, we discuss how to approximate the conditional expectation of a random variable Y given a random variable X, i.e. E (Y|X). We propose and compare two different non parametric methodologies to approximate E (Y|X). The first approach (namely the OLP method) is based on a suitable approximation of the sigma-algebra generated by X. A second procedure is based on the well known kernel non-parametric regression method. We analyze the convergence properties of the OLP estimator and we compare the two approaches with a simulation study.

On the approximation of a conditional expectation

LANDO, Tommaso;ORTOBELLI LOZZA, Sergio
2015-01-01

Abstract

In this paper, we discuss how to approximate the conditional expectation of a random variable Y given a random variable X, i.e. E (Y|X). We propose and compare two different non parametric methodologies to approximate E (Y|X). The first approach (namely the OLP method) is based on a suitable approximation of the sigma-algebra generated by X. A second procedure is based on the well known kernel non-parametric regression method. We analyze the convergence properties of the OLP estimator and we compare the two approaches with a simulation study.
journal article - articolo
2015
Lando, Tommaso; ORTOBELLI LOZZA, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/49676
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