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1779Lasso Threshold Calibration 4In an orthonormal lasso update, a coordinate has score z = -3.2 and penalty lambda = 0.7. What coefficient results after soft-thresholding?统计中等derivation未尝试免费1780Lasso Threshold Calibration 5A standardized lasso model has absolute scores (5.0, 4.0, 1.5). What is the smallest lambda that leaves only the strongest feature nonzero?统计困难derivation未尝试免费1787Ridge Effective Degrees of Freedom 2A standardized ridge model has singular-value squares d j 2 = [16, 4] and penalty lambda = 4. What is the effective degrees of freedom tr(S lambda) = sum d j 2/(d j 2+lambda)?统计中等derivation未尝试免费1793Elastic Net GroupingTwo features are almost duplicates but both are economically meaningful. Why does Elastic Net often behave better than pure Lasso here?统计中等derivation未尝试免费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1795Why the One-SE Rule Is ConservativeWhy do practitioners often prefer the one-standard-error rule over the absolute CV minimizer when selecting a regularization parameter?统计困难essay未尝试面试订阅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1798Signal Stationarity Classification 3A candidate signal is defined by X t = ε t + s t where s t is a fixed deterministic day-of-week pattern. Is it weakly stationary?统计简单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1802Measurement Noise Effect 2A latent stationary signal Y t has gamma(0) = 8 and gamma(1) = 3. You observe X t = Y t + eta t, where eta t is iid noise with variance 2 independent of Y t. What are gamma X(0) and gamma X(1)?统计中等derivation未尝试免费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1812Validity or Stationarity Check 2Consider the proposal rho(1)=1.2. Is it valid from a stationarity / autocorrelation perspective?统计中等derivation未尝试免费1813Validity or Stationarity Check 3Consider the proposal An AR(1) with phi = 1.03. Is it valid from a stationarity / autocorrelation perspective?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1816Why Differencing Helps a Trend but Not White NoiseA signal looks like deterministic trend plus short-memory noise. Why can first differencing help stationarity, while differencing plain white noise usually just injects a negative lag-1 correlation?统计简单essay未尝试免费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1818Why Ergodicity MattersWhy is ergodicity stronger than stationarity, and why do practitioners care about it when they average one long signal history?统计中等derivation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