Notes On Nonparametric Density Estimation
نویسنده
چکیده
Univariate Density Estimation via Numerical Derivatives Consider the problem of estimating the density function f(x) of a scalar, continuously-distributed i.i.d. sequence xi at a particular point x. If the density f is in a known parametric family (e.g., Gaussian), estimation of the density reduces to estimation of the finite-dimensional parameters that characterize that particular density in the parametric family. Without a parametric assumption, though, estimation of the density f over all points in its support would involve estimation of an infinite number of parameters, known in statistics as a nonparametric estimation problem (though “infinite-parametric estimation” might be a more accurate title). Since the density function f(x) is the derivative of the cumulative distribution function F (x) ≡ Pr{xi ≤ x}, and since the empirical c.d.f.
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