Abstract
In the linear model y = x′β + u where x is a regressor vector and E(u | x)= 0, we estimate β in E(y | x)= x′β However, the assumption of the linear model, or any nonlinear model for that matter, is a strong one. In nonparametric regression, we try to estimate E(y | x) without specifying the functional form. Since
if we can estimate f(y, x) and f(x), we can also estimate E(y | x). In this chapter, we study nonparametric density estimation for x as a prelude to nonparametric regression in the next chapter. We will assume that x has a continuous density function f (x) If x is discrete, one can estimate P(x = x 0) either with the same estimation method used for the continuous case or with the number of observations with x i = x 0. There are several nonparametric density estimation methods available. The most popular is “kernel density estimation method” which we explore mainly. Other methods will be examined briefly in the last section. See Prakasa Rao (1983), Silverman (1986), Izenman (1991), Rosenblatt (1991) and Scott (1992) for more on nonparametric density estimation in general.
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© 1996 Springer Science+Business Media New York
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Lee, Mj. (1996). Nonparametric Density Estimation. In: Methods of Moments and Semiparametric Econometrics for Limited Dependent Variable Models. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2550-6_7
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DOI: https://doi.org/10.1007/978-1-4757-2550-6_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2552-0
Online ISBN: 978-1-4757-2550-6
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