CAS Exam MAS-I Fall 2019, Question 29
Study guide: Exam MAS-I
An actuary has a dataset with four observations and wants to use Leave-One-Out Cross Validation (LOOCV) to determine which one of two competing models fits the data better. The model preference will be based on minimizing the mean squared error.
The values of the dependent variable are:
\mathbf{y} = [y_1, y_2, y_3, y_4] = [1.55, 1.55, 1.60, 1.95]Corresponding fitted values under each model and training data subset are:
| Training Obs. Used | Model 1 \hat{y}_1 |
Model 1 \hat{y}_2 |
Model 1 \hat{y}_3 |
Model 1 \hat{y}_4 |
Model 2 \hat{y}_1 |
Model 2 \hat{y}_2 |
Model 2 \hat{y}_3 |
Model 2 \hat{y}_4 |
|---|---|---|---|---|---|---|---|---|
| 1,2,3 | 1.50 | 1.60 | 1.20 | 1.80 | 1.60 | 1.70 | 1.60 | Z |
| 1,2,4 | 2.00 | 1.50 | 1.10 | 1.90 | 1.80 | 1.40 | 1.30 | 1.70 |
| 1,3,4 | 1.75 | 1.55 | 1.70 | 2.10 | 1.40 | 1.30 | 1.50 | 1.95 |
| 2,3,4 | 1.70 | 1.65 | 1.60 | 2.00 | 1.60 | 1.70 | 1.20 | 2.00 |
Calculate the maximum value of Z for which the actuary will prefer Model 2.
- A) Less than 1.5
- B) At least 1.5, but less than 1.8
- C) At least 1.8, but less than 2.1
- D) At least 2.1, but less than 2.4
- E) At least 2.4
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