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1928Minimum Detectable Edge 3Using the same approximation n >= K * sigma 2 / delta 2, suppose K = 9, sigma = 30 bp, and you can collect only n = 900 observations. What is the smallest detectable mean edge delta, in basis points?统计中等数值题未尝试免费1931Effective Sample Under Serial Dependence 1A return series has 240 observations and lag-1 autocorrelation 1/5. Using the heuristic n eff = n * (1-rho)/(1+rho), what is the effective sample size?统计简单essay未尝试免费1936Paired Design Observation Ratio 1Two strategies are tested on the same names and dates, giving correlation 1/5 between their noise terms. Relative to an unpaired comparison with the same marginal variance, by what factor does the paired design reduce required sample size?统计简单数值题未尝试免费1941Power Score Design Choice 1Compare two research designs using the score delta * sqrt(n) / sigma. Design A has delta=4 bp, n=225, sigma=2 bp. Design B has delta=3 bp, n=400, sigma=1 bp. Which design has the larger score?统计简单数值题未尝试免费6013Power of a One-Sided Z-TestYou run a one-sided z-test at level alpha = 0.05 (critical value 1.645) for a positive mean edge. The true edge is delta = 3 bp, the per-observation standard deviation is sigma = 8 bp, and you collect n = 64 observations. The power equals Phi(delta*sqrt(n)/sigma - 1.645). Compute the power, using Phi(1.355) approx 0.9123.统计中等数值题未尝试免费6014Quadrupling the SampleYour current backtest detects a minimum edge of 6 bp at the desired power. You extend the sample so the number of observations is multiplied by 4, keeping sigma, alpha, and target power fixed. Because the minimum detectable effect scales as 1/sqrt(n), what is the new minimum detectable edge, in basis points?统计简单数值题未尝试免费6015Track Record to Confirm a SharpeA strategy has a true annualized Sharpe ratio of 0.5. The t-statistic of the mean return over a track record of T years is approximately t = SR * sqrt(T). How many years of returns are needed before the t-statistic reaches 2 (the usual significance bar)?统计中等数值题未尝试免费