Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why is the variance of the Parzen density estimator infinite?

  1. Sep 19, 2010 #1
    Hello everyone,

    I'm new to this forum and I'm glad to have found such a high quality resource where we can have such valuable guidance and discussions.

    I've read somewhere that the variance of [tex]p(x) = {\frac{1}{n}}\sum_{i=1}^{n}\delta(x-x_i) \forall x \in \Re[\tex],

    in which [tex]D_n = \left\{x_1, \cdots, x_n\right\}[\tex] independent realizations of a continuous random variable [tex]X[\tex], and [tex]\delta[\tex] is the dirac delta function, is infinite, irrespective to [tex]n[\tex] and [tex]D_n[\tex].

    My questions are straightforward:

    1) Why is that (my guess that the integral involved in the variance calculation does not converge)?;

    2) What does it mean to have infinite variance in practical terms?;

    3) Any practical examples where a distribution with infinite variance would be useful?;

    Please note that I don't have a strong background in statistics.

    Any help will be much appreciated.

    Last edited: Sep 19, 2010
  2. jcsd
  3. Sep 20, 2010 #2
    Assuming you mean to find the variance of the random variable with density p(x), this would be infinite only if the variance of X is infinite (for example if X has the Cauchy or Pareto distribution).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Why is the variance of the Parzen density estimator infinite?
  1. Variance of estimator (Replies: 2)