Chapter 7 · Section 2 practice

Quantile and Conformal Prediction

0 of 3 answered

These questions review the examples in the companion slides. Choose an answer, then check the explanation.

Question 1

Which constant \(q\) minimises \(\mathbb E[\ell_\tau(y, q)]\)?

  • The mean of \(y\)
  • The \(\tau\)-quantile of \(y\) — the loss is asymmetric by exactly the odds \(\tau : (1-\tau)\)
  • The median, for every \(\tau\)
  • The mode

Question 2

The 90 % band \([\hat q_{0.05}, \hat q_{0.95}]\) should contain \(y\) on 90 % of days. Where will empirical coverage be lowest?

  • Training rows — the model has not converged
  • All three near 0.90 — the loss guarantees it
  • Test rows — the band is tuned to the training data and 2020 is a new regime
  • Calibration rows — 2019 was unusually calm

Question 3

Coverage fell to 0.18 in March 2020. What failed?

  • The quantile model — its trees were under-fitted
  • The exchangeability assumption — 2019’s scores say nothing about March 2020’s
  • The formula for \(k\) — it should use \(n\), not \(n + 1\)
  • The target \(\alpha\) — 0.10 is too ambitious for daily returns