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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 →MLE · 假设检验 · 置信区间 · Bootstrap
打开 →上海某私募的量化研究员把上一课跑出来的两个候选估计量并排放着:一个是无偏的样本方差 公式(分母 公式),另一个是极大似然估计(maximum likelihood estimation, MLE)的方差版 公式(分母 公式)。直觉告诉他「无偏」听起来更值得信赖,但当真到了要在波动率模型里塞一个数,他需要的是一把明确可比较的「好坏」尺子——能告诉他在 公式 的...
打开 →周三晚上，某 私募 宏观对冲基金的策略会议上，研究员摔出一张图：「2Y CGB 收益率比 10Y 还高了 8bp，曲线倒挂了。要不要做平 2 10 利差？」要回答这个问题，你得先把「2Y vs 10Y」这两个点背后的曲线讲清楚——它是怎么画出来的、上面的点对应的是哪种「率」、不同形状对应什么宏观状态。本课把这条曲线建起来。 曲线是什么 收益率曲线（yield...
打开 →周五下午两点半，浦东陆家嘴一家中型私募的风控会上，PM 把昨晚跑出来的 tear sheet 推过来：「食品饮料这只 600519.SH 的 63 日滚动 夏普比率 （Sharpe ratio）样本期均值是 0.86，银行那两只 000001.SZ 和 600036.SH 是 0.42。0.44 的差，可信吗？」你脑子里第一反应是 3.2.2 L5 那...
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?
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