On the Approximation of a Conditional Expectation
نویسنده
چکیده
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 σ-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. Key-Words: Conditional Expectation, Kernel, Non Parametric methods, Regression, Approximation, Simulation.
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