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

Which statement about the choice of kernel function and bandwidth in non-parametric density estimation is most accurate?

The bandwidth drives the bias-variance trade-off and generally matters more than which kernel is used. Small bandwidths reduce bias but raise variance, while large ones do the opposite, so a smaller bandwidth is not always better.

  1. AThe kernel shape matters far more than the bandwidth for the quality of the estimate
  2. BThe bandwidth governs the bias-variance trade-off and usually matters more than the specific kernel chosenCorrect
  3. CA smaller bandwidth always gives lower estimation error
  4. DThe bandwidth must equal the sample standard deviation

Explanation

Bandwidth controls the trade-off: small values give low bias but high variance, large values the reverse. Common kernels give similar results for a sensible bandwidth. Smaller is not always better, and no rule fixes the bandwidth at the standard deviation.

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