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1764Selection Bias from Looking Only at Filled OrdersA desk studies how aggressiveness X affects trade profitability Y, but Y is observed only for orders that actually fill. Fill probability is higher when latent market demand D is strong, and stronger demand also tends to improve profitability. Why can regressing observed Y on X using only filled orders be biased?统计中等multi part未尝试面试订阅1765Fixed Effects Still Miss a Moving Stress ChannelPanel fixed effects remove each desk's persistent skill, but an omitted intraday stress variable still changes day by day. Suppose higher stress raises both inventory pressure X and slippage Y within the same desk. After adding desk fixed effects, what confounding channel remains, and in what direction does it bias the within-desk slope on X?统计中等essay未尝试面试订阅1766What Remains After Controlling the Hedge ChannelA signal X changes the hedge ratio H immediately, and both X and H affect desk PnL Y. The direct effect of X on Y is +1.2 bps, while the channel through H contributes another +0.8 bps. If H is measured perfectly and you regress Y on X and H, what effect does the coefficient on X identify, and what number should it equal?统计简单derivation未尝试免费1767Weak-IV Risk From the First Stage AloneA proposed instrument shifts treatment by 0.02 with standard error 0.015 in the first stage. Even if the exclusion story sounds plausible, what first-stage F-statistic do you get, and what is the main identification concern?统计中等derivation未尝试面试订阅1768A Lagged Variable Is Not Automatically a Valid InstrumentSomeone proposes using yesterday's order-flow imbalance as an instrument for today's imbalance in a return-impact regression. Why is this not automatically a valid instrument in financial data?统计中等multi part未尝试面试订阅1770Why Selection on Implemented Trades Distorts Treatment EffectsWhy can studying only executed trades bias the estimated effect of an execution rule, even if the rule assignment itself was randomized upstream?统计简单essay未尝试免费1777Lasso Threshold Calibration 2A standardized lasso fit has absolute score magnitudes (3.8, 2.5, 0.9). What is the smallest lambda that zeroes the weakest feature while leaving the other two still active?统计简单essay未尝试免费1790Ridge Effective Degrees of Freedom 5A standardized ridge model has singular-value squares d j 2 = [12.25, 4, 0.25] and penalty lambda = 0.25. What is the effective degrees of freedom tr(S lambda) = sum d j 2/(d j 2+lambda)?统计困难derivation未尝试面试订阅1794Duplicate Feature Under Pure LassoIf two predictors are exactly identical and the model uses pure Lasso, what modeling pathology should you expect?统计中等essay未尝试免费1797Signal Stationarity Classification 2A candidate signal is defined by X t = 0.2 t + ε t. Is it weakly stationary?统计中等derivation未尝试免费1800Signal Stationarity Classification 5A candidate signal is defined by X t = t ε t. Is it weakly stationary?统计困难derivation未尝试面试订阅1803Measurement Noise Effect 3A latent stationary signal Y t has gamma(0) = 6 and gamma(1) = -1. You observe X t = Y t + eta t, where eta t is iid noise with variance 4 independent of Y t. What are gamma X(0) and gamma X(1)?统计中等derivation未尝试免费1808Two-Point Sample Mean Variance 3A weakly stationary process has gamma(0) = 5 and gamma(1) = -1. What is Var((X 1 + X 2)/2)?统计中等数值题未尝试免费1814Validity or Stationarity Check 4Consider the proposal An AR(1) with phi = -0.6. Is it valid from a stationarity / autocorrelation perspective?统计困难derivation未尝试面试订阅1815Validity or Stationarity Check 5Consider the proposal An MA(1) claiming rho(1)=0.7. Is it valid from a stationarity / autocorrelation perspective?统计困难数值题未尝试面试订阅1817Spurious Regression WarningWhy can regressing one drifting series on another produce a large R-squared and tiny p-values even when there is no economic relation?统计简单essay未尝试免费1819Ljung-Box InterpretationWhat null hypothesis does the Ljung-Box test target in a return series, and what practical concern does rejection raise?统计中等derivation未尝试免费1820Measurement Noise Flattens ACFWhy can adding independent observation noise make an otherwise persistent signal look less autocorrelated?统计困难derivation未尝试面试订阅1833MA(1) Invertibility Check 3An MA(1) execution-noise model uses theta = -0.7. Is the model invertible?统计中等数值题未尝试面试订阅1843ARMA Identification or Simplification 3You observe the diagnostic statement: Both ACF and PACF tail off. What is the correct modeling conclusion?统计中等derivation未尝试面试订阅