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FRM Part II · FRM Exam Part II · Non-parametric Approaches

An analyst compares a rectangular (uniform) kernel with a Gaussian kernel, each with the same bandwidth parameter, for estimating a density from 300 return observations. Which statement is most accurate?

Bandwidth normally has a far greater influence on a kernel density estimate than kernel shape. A smooth kernel such as the Gaussian gives a smoother curve than a uniform kernel, but it does not assume normal returns, and a uniform kernel remains usable for quantiles.

  1. AThe uniform kernel gives a smoother density estimate because all points in the window get equal weight
  2. BThe choice of kernel shape usually matters far less than the choice of bandwidth, though smoother kernels yield smoother estimatesCorrect
  3. CThe Gaussian kernel requires the underlying returns to be normally distributed for the estimate to be valid
  4. DThe uniform kernel cannot be used for quantile estimation because it is discontinuous

Explanation

Practical results are typically much more sensitive to bandwidth than to kernel shape. A Gaussian kernel is smooth, but using it does not assume normal data, and a uniform kernel still produces a valid, though less smooth, estimate. So only the second statement holds.

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