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1701Holm Improvement Needed for All Three Themes to PassThree ordered family p-values are 0.012, 0.027, and 0.030. The desk uses Holm at 5% family-wise error. By how much must the middle p-value fall so that all three themes pass?统计中等derivation未尝试面试订阅1702Median of the Smallest Null p-Value Across 25 TriesA researcher always reports the smallest p-value among 25 genuinely null backtests. Under independence and exact Uniform(0,1) null p-values, what is the median of that reported minimum?统计简单derivation未尝试免费1703False Positives from Daily Strategy MiningSuppose you test 20 pure-noise trading rules every day for 252 trading days, always at level 5% and without any adjustment. How many false positives do you expect over the full year?统计简单derivation未尝试免费1704In-Sample Screen Needed After a 10-Lag SearchA desk tries 10 lags for a genuinely null signal, keeps the best in-sample lag if any lag has p-value below alpha, and then requires a fresh holdout p-value below 10%. What alpha makes the overall false-launch probability exactly 2%, assuming independence under the null?统计简单derivation未尝试免费1705FWER or FDR for a Large Exploratory Screen?You are screening 500 candidate alphas and expect only a handful to survive practical checks. Is FWER control or FDR control usually the more natural starting point, and why?统计中等essay未尝试面试订阅1706Why Dependence Changes the Adjustment, Not the ProblemA PM tests 40 signals built from only a few common macro themes, so the p-values are strongly dependent. Why is 'just divide alpha by 40' often too crude, and what is the right conceptual response?统计简单essay未尝试免费1707Why Hierarchical Testing Can HelpA researcher first tests whether a sector shows any effect, and only if that passes does she test stocks inside that sector. Why can this hierarchical design reduce the multiplicity burden?统计中等essay未尝试面试订阅1708What BH Actually ControlsAt Benjamini-Hochberg target q=0.10, you end up rejecting 5 hypotheses. Does the method guarantee that exactly 10% of those 5 are false discoveries?统计中等essay未尝试面试订阅1709Dependence Can Reduce Effective MultiplicitySuppose 100 candidate factors collapse into roughly 20 tight clusters of nearly identical signals. What qualitative effect does this have on multiplicity relative to 100 truly independent tests?统计中等essay未尝试面试订阅1710Global Error Implied by a Per-Bucket CutoffA desk uses the same per-bucket cutoff 0.0045 across 20 independent event buckets. What family-wise false-positive probability does that imply?统计中等derivation未尝试面试订阅1711Backtest Slide Misreads p = 0.03A PM deck says: ‘The event-study p-value is 0.03, so there is a 97% probability the signal is real.’ What is the statistical mistake?统计简单essay未尝试免费1712Statistical Significance Is Not Economic SignificanceWith millions of observations, a strategy's average edge is estimated at 0.2 basis points and is highly statistically significant. Why is 'highly significant' not enough to conclude the strategy matters economically?统计简单essay未尝试免费1713No Significance Is Not No EffectA small-cap execution pilot reports p = 0.18 and the note says ‘there is no effect, so we should stop the project.’ Why is that too strong?统计简单essay未尝试免费1714Optional Stopping as a p-Hacking MechanismA PM checks the p-value every hour and stops the experiment as soon as p < 0.05. Why does this inflate false positives?统计中等essay未尝试面试订阅1715The Prosecutor's Fallacy in a Trading ContextA rare anomaly occurs in only 1 out of 10,000 normal days. A model flags today's pattern as one that would happen with probability 1/10,000 under the null, and someone concludes the null must almost certainly be false. What key base-rate issue are they missing?统计中等essay未尝试面试订阅1716Replication Probability Is Not 1 - pA researcher says: ‘This alpha had p = 0.04, so replication next quarter is 96% likely.’ Why is that interpretation invalid?统计简单essay未尝试免费1717Significant but Commercially UncertainA venue-routing tweak delivers p = 0.01, but the 95% confidence interval for annual savings is [10k, 1.2m]. Why should the team still be cautious?统计简单essay未尝试免费1718Best-of-50 Reporting Without AdjustmentA researcher tests 50 candidate features and only reports the one with the smallest p-value, which happens to be 0.01. Why is it misleading to present 0.01 as if it came from a single pre-specified test?统计中等essay未尝试面试订阅17190.049 vs 0.051 Decision CliffTwo backtests differ only slightly: one reports p = 0.049 and the other p = 0.051. Why is it bad practice to call one ‘real’ and the other ‘not real’ purely because one is below 0.05?统计简单essay未尝试免费1720Low Prior Probability and Positive Predictive ValueSuppose only 1% of tested trading ideas are genuinely predictive. A testing pipeline has 80% power and a 5% false-positive rate. Conditional on obtaining a positive result, what fraction of positives are truly real?统计中等derivation未尝试面试订阅