题目1748 · 统计
Fitted Variance From R-Squared and Response Variance
A regression with intercept has response variance 9 and R^2 = 4/9. What is the variance of the fitted values?
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中文题目题目5848 · 金融与交易
Short Straddle Profit and Risk
You sell (write) a straddle at strike 100, collecting a call premium of 6 and a put premium of 7. What is the maximum profit, the two break-even prices, and the profit if the stock ends at 118?
打开 →题目2713 · 机器学习
Why High-Turnover Strategies Are Easier to Overfit
Why does backtest overfit become especially dangerous for very high-turnover strategies?
打开 →题目2718 · 机器学习
Why Strategy Combination Can Also Overfit
Why does building a meta-portfolio from many individually researched strategies create another layer of overfitting risk?
打开 →题目5803 · 金融与交易
Minimum Width For A Profit Target
A maker wants to earn at least 5.0 in total net edge over a session in which it expects exactly 250 fills. Each fill earns (h - loss) with adverse-selection loss 0.008, and the maker assumes the fill count is independent of the half-spread over the relevant range. What is the min
打开 →题目4440 · 机器学习
Before Refitting More Often
What should you check first before increasing refit frequency because recent performance dipped?
打开 →题目1684 · 统计
Chi-Square Goodness-of-Fit for a Die
A six-sided die is rolled 60 times, and the counts are $(14,8,11,9,10,8)$. Test fairness using a chi-square goodness-of-fit test.
打开 →题目2649 · 机器学习
How Many Expanding-Window Folds Fit in a Monthly Panel?
You have 60 months of data. Each expanding-window fold uses 24 months for training, the next 6 months for validation, and then advances by 6 months. How many validation folds fit?
打开 →题目2400 · 机器学习
How Many Independent Fits to Hit a Variance Target
Each independently trained model has variance 2.4 and negligible bias. How many equally weighted independent fits must you average to bring the variance term below 0.3?
打开 →题目2646 · 机器学习
Model-Fit Count in a Nested CV Search
A team runs 5 outer folds. Inside each outer-training split, it evaluates 6 hyperparameter settings by 4-fold CV, then refits the chosen model once on the full outer-training split. How many total model fits are performed?
打开 →题目4425 · 机器学习
Monthly Refit Count With Quarterly Test Blocks 10
A walk-forward process uses 24 months of initial training and then evaluates 3-month test blocks, advancing the whole scheme by 1 month each time through a total history of 39 months. How many model refits are performed?
打开 →题目4368 · 机器学习
Nested CV Fit Count 3
Successive halving starts with 27 configurations. Each round keeps one third of the configurations and evaluates all survivors once. If you run three rounds total, how many model fits are executed?
打开 →题目4370 · 机器学习
Nested CV Fit Count 5
A time-series hyperparameter sweep evaluates 8 settings on 6 expanding-window splits. If each setting is refit once per split, how many model fits are needed?
打开 →题目5983 · 概率
Number of Trades to Cross a Profit Target
A strategy books i.i.d. positive profits $X_1,X_2,\dots$ with $E[X_i]=2.5$. Let $N$ be the first time the running total $S_n=\sum_{i=1}^n X_i$ strictly exceeds $10$; that is, $N=\min\{n:S_n>10\}$. Assuming $E[N]<\infty$, the expected overshoot is known to satisfy $E[S_N]=14$. Use
打开 →题目3234 · 统计
Partial Pooling Versus Separate Fits
Why does a hierarchical Bayesian model for many related assets often produce more stable estimates than fitting each asset separately and then testing them one by one?
打开 →题目3225 · 统计
Posterior Predictive Check Versus Classical Goodness-of-Fit
Why does a posterior predictive check answer a different question from a classical goodness-of-fit p-value?
打开 →题目2493 · 机器学习
Projection Error Is Orthogonal to the Fitted Subspace 23
Why is y - X beta_hat orthogonal to every fitted vector Xv?
打开 →题目4427 · 机器学习
Refit Cadence
Why can refitting every single day be worse than refitting monthly, even when more frequent updating sounds adaptive?
打开 →题目4435 · 机器学习
Refitting Less Often
If you refit less often in a stable regime, what usually happens to turnover of the model parameters?
打开 →题目2447 · 机器学习
Shift in the Training Mean After Fitting a Scaler on All Rows
A feature has training mean 10 over 80 rows and test mean 14 over 20 rows. A scaler is wrongly fit on all 100 rows and uses standard deviation 5. What is the average standardized value of the training block under that leaked fit?
打开 →题目1751 · 统计
Slope and Intercept From Two Fitted Benchmarks
A desk summarizes its fitted line by saying y_hat = 2.4 when x = 1 and y_hat = 0.9 when x = 6. What are the slope and intercept of the line?
打开 →题目1741 · 统计
Slope From Fitted Energy and Predictor Energy
In a simple OLS regression with intercept, the centered predictor sum of squares is S_xx = 20 and the fitted values have centered sum of squares 45. If the slope is known to be positive, what is the OLS slope?
打开 →题目1746 · 统计
Slope From Predictor Variance and Fitted Variance
In a simple OLS regression with intercept, x has sample variance 9 and the fitted values have sample variance 4. If the slope is positive, what is the slope coefficient?
打开 →题目3828 · 金融与交易
Who Benefits If Current Par Exceeds Contract Fixed
If the current par swap rate is above the contract fixed coupon, which side benefits: payer fixed or receiver fixed?
打开 →题目3829 · 金融与交易
Who Benefits If Current Par Is Below Contract Fixed
If the current par swap rate is below the contract fixed coupon, which side benefits?
打开 →题目2580 · 机器学习
Why More Trees Usually Do Not Create Classical Overfit 15
Why does adding more trees to a random forest typically plateau rather than create the kind of explosive overfit seen in some single-model families?
打开 →题目1754 · 统计
Why Multicollinearity Can Leave Training Fit Looking Fine
Why can a regression with severe multicollinearity still show a strong in-sample fit and a high R^2?
打开 →题目4448 · 机器学习
Correlation Shock Benefit 8
An equal-weight composite combines two standardized signals. If their correlation drops from 0.6 to 0.2, by how much does the composite standard deviation fall?
打开 →题目5810 · 金融与交易
Expected Profit Over N Quotes
Over a session you post 5000 quotes. Each quote has a fill probability of 0.08, and each fill earns a net edge of 0.25. What is your expected total PnL for the session?
打开 →题目4366 · 机器学习
Nested CV Fit Count 1
Three model sizes have mean CV AUCs 0.790, 0.802, and 0.808. The standard error of the best score is 0.010. Under the one-standard-error rule, which is the simplest model you would keep?
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