Actuarial Notes

CAS Exam MAS-I Fall 2018, Question 37

Study guide: Exam MAS-I

You are estimating the coefficients of a linear regression model by minimizing the sum:

\sum_{i=1}^{n}\left(y_i - \beta_0 - \sum_{j=1}^{p}\beta_j x_{ij}\right)^2 + \lambda\sum_{j=1}^{p}|\beta_j|

From this model you have produced the following plot of various statistics as a function of tuning parameters, \lambda:

Determine which of the following statistics X and Y represent.

  • A) X = Squared Bias, Y = Training MSE
  • B) X = Test MSE, Y = Training MSE
  • C) X = Test MSE, Y = Variance
  • D) X = Training MSE, Y = Variance
  • E) X = Variance, Y = Test MSE

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