STA305H1 Lecture Notes - Lecture 15: Kernel Density Estimation, Empirical Distribution Function, Density Estimation
18 Jan 2018
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Document Summary
Suppose we observe independent random variables x1, , xn, which we believe are a ran- dom sample from some distribution function f whose form is unknown. Previously, we de ned a simple estimator of f , namely the empirical distribution function: (cid:2)f (x) = For a given value of x, (cid:2)f (x) is simply the proportion of the data less than or equal to x. In many situtions, it may be reasonable to assume that f is a continous distribution function, in which case it may be useful to estimate the density function f corresponding to. Recall that the density function is a non-negative function that satis es the equation. F (x) =(cid:4) x f (t) dt for all x; we can also think of f (x) as the derivative of f (x). Previously, we considered heuristic methods for estimating the density using the spacings but noted that these methods do have some non-trivial drawbacks.
