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1 Markets I: The Ecosystem and Exchange-Traded Marketsالأسواق عبر الإنترنت 2 Markets II: Rates, FX and Creditالأسواق عبر الإنترنت 3 Markets III: Commodities, Energy and Cryptoالأسواق عبر الإنترنت 4 Quantitative Methodsالأساليب عبر الإنترنت 5 Derivatives and Volatilityالمشتقات عبر الإنترنت 6 Rates, Credit, XVA and Riskالفائدة والائتمان والمخاطر عبر الإنترنت 7 Research Craft: Predictors, Backtests, Measurement, Portfoliosالبحث عبر الإنترنت 8 Strategies I: Equities and Futuresالاستراتيجيات عبر الإنترنت 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desksالاستراتيجيات عبر الإنترنت 10 Microstructure and Executionالتنفيذ عبر الإنترنت 11 Market Making and High-Frequency Tradingصناعة السوق عبر الإنترنت 12 Machine Learning for Marketsتعلم الآلة عبر الإنترنت 13 Low-Latency Softwareالتكنولوجيا عبر الإنترنت 14 Networks, Hardware and Trading Infrastructureالتكنولوجيا عبر الإنترنت 15 Research, Data and Risk Platformsالتكنولوجيا عبر الإنترنت 16 The Desk and the Firmالشركة عبر الإنترنت 17 The Industry: Firms, Roles and Careersالمسارات المهنية عبر الإنترنت 18 The Interview Bookالمسارات المهنية عبر الإنترنت
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Quantitative Finance · المسرد

ما معنى False discovery rate, Benjamini–Hochberg procedure؟

يُعرف أيضًا باسم: false discovery rate · Benjamini--Hochberg procedure

Definition 12.11 Quantitative Methods · الفصل 12 — Testing and Multiple Testing

If a procedure makes RR rejections of which VV are true nulls, its false discovery rate is E[V/max⁡(R,1)]\E[V/\max(R, 1)]. The Benjamini–Hochberg procedure at level qq rejects H(1),…,H(k)H_{(1)}, \dots, H_{(k)} for the largest kk with p(k)≤kq/mp_{(k)} \le kq/m.

A thousand signals, a hundred of them real: average true and false discoveries of four rules at 5%. No correction: 91 true, 45 false. Bonferroni and Holm: 18 true, 0.05 false. Benjamini–Hochberg: 61 true, 2.9 false (a false discovery rate of 4.4%). Data: the chapter’s tutorial, seeded.
Figure 12.4. A thousand signals, a hundred of them real: average true and false discoveries of four rules at 5%. No correction: 91 true, 45 false. Bonferroni and Holm: 18 true, 0.05 false. Benjamini–Hochberg: 61 true, 2.9 false (a false discovery rate of 4.4%). Data: the chapter’s tutorial, seeded.

أمثلة

Example 12.13 (Five pp-values)

Take p=(0.005,0.01,0.03,0.04,0.2)p = (0.005, 0.01, 0.03, 0.04, 0.2) and α=q=5%\alpha = q = 5\%. Bonferroni’s threshold 0.010.01 rejects two. Holm compares them in order with 0.05/5,0.05/4,0.05/3,…0.05/5, 0.05/4, 0.05/3, \dots: 0.005≤0.010.005 \le 0.01 and 0.01≤0.01250.01 \le 0.0125, then 0.03>0.01670.03 > 0.0167 stops it at two. Benjamini–Hochberg compares with 0.01,0.02,0.03,0.04,0.050.01, 0.02, 0.03, 0.04, 0.05: the largest kk with p(k)≤0.01kp_{(k)} \le 0.01k is k=4k = 4, so it rejects four. As adjusted pp-values (the smallest level at which each is rejected): Bonferroni (0.025,0.05,0.15,0.2,1)(0.025, 0.05, 0.15, 0.2, 1), Holm (0.025,0.04,0.09,0.09,0.2)(0.025, 0.04, 0.09, 0.09, 0.2), Benjamini–Hochberg (0.025,0.025,0.05,0.05,0.2)(0.025, 0.025, 0.05, 0.05, 0.2).

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