Chapter 7 quiz

Modern Statistical Learning in Practice

0 of 10 answered

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

Question 1

Take a prediction \(\hat y\) and replace it by \(3\tanh(50\hat y)\) — strictly increasing, very different values. What happens to the top-20 / bottom-20 portfolio and to the MSE?

  • Both change — the portfolio depends on the size of the predictions
  • Portfolio changes, MSE is unchanged
  • Portfolio is identical, MSE can change by orders of magnitude
  • Nothing changes — MSE is invariant to monotone transforms

Question 2

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 3

The choices refer to treating the linear nuisance fits as correctly specified conditional means.

OLS with \(X\) as controls assumes…

  • \(X\) is uncorrelated with \(D\)
  • \(X\) has no effect on \(Y\)
  • \(\mathbb E[Y \mid X]\) and \(\mathbb E[D \mid X]\) are linear in \(X\) — a curved confounder leaks through
  • Nothing — controls always close the backdoor path

Question 4

For 21 correlated ETFs on 251 daily returns, the condition number \(\lambda_{\max}/\lambda_{\min}\) of the sample covariance will be of the order of…

  • 1–10: daily returns are nearly uncorrelated
  • 50–100
  • Thousands — the smallest eigenvalues are almost pure noise
  • Infinite — 21 assets need more than 251 days to invert

Question 5

The fixed-horizon label \(\mathbb 1[r_{t \to t+10} > 0]\) ignores…

  • The sign of the return
  • The horizon — 10 days is arbitrary
  • The path: a trade stopped out on day 3 can still end positive on day 10
  • Nothing — it is the label every paper uses

Question 6

A colleague reports: “the best of my 40 rules has Sharpe 1.1 over ten years.” Is that evidence the rule works?

  • Yes — 1.1 over ten years is t = 3.5, far beyond 2
  • Yes, if the rule has an economic story
  • No — nothing that comes from a search can be evidence
  • Not by itself — the expected best of 40 noise trials is already above 0.6; the answer needs \(N\), the trial variance, \(T\), skew and kurtosis

Question 7

The retrieved passage has the highest similarity. What should the assistant do next?

  • Copy it because it comes from the course
  • Check its status and explanation, adapt the corrected pattern, then test the task
  • Increase the number of retrieved passages and accept the majority answer

Question 8

Replacing ret_next by its within-month percentile changes…

  • Nothing — a linear model on ranks has the same order of predictions as a linear model on returns
  • The weighting of months: the ±80 % months no longer dominate the fit
  • The model class — ranks require a classifier
  • The features — they must be ranked too

Question 9

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 10

Scope: the fitted same-row learner in this chapter’s seeded example. The direction of bias is not a universal property of same-row residuals.

Fit \(\hat m\) and \(\hat\ell\) on all \(n\) rows with a learner flexible enough to memorise, then compute \(\hat\theta\) on the same rows. The estimate will be…

  • Unbiased — more data for the nuisance models can only help
  • Biased toward zero — the in-sample residuals of \(D\) have absorbed the noise that identifies \(\theta\)
  • Biased away from zero — overfitting inflates every coefficient
  • Undefined — the residuals are exactly zero