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1696Expected False Finalists After a Lookback FunnelA desk studies 30 genuinely null signals. For each signal it tries 4 lookback windows, advances the signal if any in-sample p-value is below 10%, and then requires a fresh holdout p-value below 5%. Assuming independence under the null, what is the expected number of false finalists?统计简单derivation未尝试免费1697Any False Sector Winner After Within-Sector MiningA desk has 12 sectors, each containing 5 genuinely null variants. In each sector it keeps only the smallest p-value, and it flags the sector if that winning p-value is below 1%. Assuming independence, what is the probability at least one sector is falsely flagged?统计简单derivation未尝试免费1698Bonferroni Cutoff After Collapsing to Effective FamiliesA research grid contains 60 model variants, but the desk argues they amount to only 15 effectively distinct families. If it wants family-wise error at most 10% using a Bonferroni family-level rule, what p-value cutoff should it apply to each effective family?统计中等derivation未尝试面试订阅1699Sidak Cutoff for 18 Effective Research ChoicesA desk believes its many correlated parameter tweaks boil down to 18 effectively independent research choices. What Sidak per-choice cutoff controls family-wise error at 5%?统计简单derivation未尝试免费1700BH q Range That Keeps Exactly Three FamiliesFive family-level winners have ordered p-values 0.004, 0.011, 0.018, 0.031, and 0.070. For what range of BH target levels q would Benjamini-Hochberg keep exactly the first three discoveries?统计中等derivation未尝试面试订阅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