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中文题目A sample is {1,4}. Under the nonparametric bootstrap with resample size 2, compute the bootstrap expectation of the sample maximum and the resulting bootstrap bias estimate for the original maximum statistic.
打开 →A sample of size n has empirical success rate p_hat. Under the nonparametric bootstrap, what is the variance of the resampled sample mean conditional on the observed data?
打开 →A sample is {a,b}. In the nonparametric bootstrap, a resample of size 2 is drawn with replacement. Derive the variance of the bootstrap sample mean.
打开 →If a statistic is the sample mean and you use an m-out-of-n nonparametric bootstrap instead of an n-out-of-n bootstrap, how does the conditional variance of the resampled mean scale with m?
打开 →Why can a residual bootstrap be invalid for regression under heteroskedasticity while a pairs bootstrap remains defensible?
打开 →When can a parametric bootstrap be more informative than a nonparametric bootstrap?
打开 →A sample is {0,0,10}. Under the nonparametric bootstrap with resample size 3, what values can the bootstrap median take, and what condition determines which one occurs?
打开 →Why is the point of a block bootstrap not merely to resample larger chunks, but to preserve local serial dependence?
打开 →Why does curve bootstrapping solve short maturities first and then move outward one maturity at a time?
打开 →Why can a bootstrap study itself become overfit if you repeatedly choose tuning knobs by looking at the same resampled diagnostics?
打开 →What conceptual idea makes the basic bootstrap interval differ from the percentile interval?
打开 →Why is the nonparametric bootstrap often too optimistic about tail risk when the observed sample contains no truly extreme events?
打开 →An estimator is constrained to be nonnegative and lands exactly at 0 on the observed sample. Why can the naive nonparametric bootstrap badly misrepresent uncertainty near that boundary?
打开 →A tabular Q-learning step starts from old Q=0, uses learning rate alpha=0.5, reward 0.1, and discount gamma=0.99. After the update the Q-value becomes 3. What max_a' Q(s',a') must the learner have used?
打开 →A tabular Q-learning step starts from old Q=0.2, uses learning rate alpha=1, reward 0.5, and discount gamma=0.9. After the update the Q-value becomes 2.9. What max_a' Q(s',a') must the learner have used?
打开 →A tabular Q-learning step starts from old Q=1.1, uses learning rate alpha=0.5, reward 0.2, and discount gamma=0.8. After the update the Q-value becomes 1.6. What max_a' Q(s',a') must the learner have used?
打开 →A tabular Q-learning step starts from old Q=-0.4, uses learning rate alpha=0.25, reward 1, and discount gamma=0.95. After the update the Q-value becomes 1.2. What max_a' Q(s',a') must the learner have used?
打开 →A tabular Q-learning step starts from old Q=0.7, uses learning rate alpha=0.4, reward 0.3, and discount gamma=0.9. After the update the Q-value becomes 2. What max_a' Q(s',a') must the learner have used?
打开 →Why should a practitioner resample accounts, users, or securities rather than individual rows when observations inside each group share latent shocks?
打开 →Why can bootstrapping help value estimates even before an episode terminates?
打开 →Why can off-policy learning become fragile when function approximation, bootstrapping, and distribution shift all interact?
打开 →Why can studentizing a bootstrap statistic improve interval accuracy in skewed or scale-varying problems?
打开 →Why can a percentile bootstrap interval end up noticeably off-center relative to the original estimate when the statistic is skewed?
打开 →Why does increasing the discount factor often make value estimates more sensitive to long-run model misspecification?
打开 →A 1.5-year bond with face 100 has annual coupon rate 4.0%, paid semiannually, and trades at 100.911. The discount factors are D(0.5)=0.985 and D(1.0)=0.968. Assume the annual-compounded forward rate from 1.0 years to 1.5 years is flat over that stub. What forward rate is implied?
打开 →Why should a quant be careful when mapping a toy MDP intuition directly into live trading?
打开 →Why does an RL agent usually need explicit exploration even if its current greedy action already looks good?
打开 →If c>0 in exp(x)+cx=d, why is the Newton denominator never zero?
打开 →Why is understanding the whole curve more useful for fixed-income trading than memorizing one quoted yield?
打开 →Why can two different zero curves generate similar par yields at some maturity?
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