Casualty Actuarial Society MAS-1 Practice Exam

In a smoothing spline model fit to data, what happens to bias as the tuning parameter lambda increases?

True False It depends on the data The bias remains unchanged

Correct Answer:

True

Explanation:

In a smoothing spline, lambda controls how strongly we favor smoothness versus fidelity to the data. A larger lambda puts more weight on the roughness penalty, so the fitted curve becomes smoother and less flexible. That reduced flexibility means the model may not capture all the true features of the underlying function, which increases the systematic error—or bias—of the fit. At the same time, variance tends to decrease because the fit is less sensitive to random noise. So as lambda increases, bias increases. In the extreme, a very large lambda forces a very smooth (often nearly straight) curve, which typically has higher bias if the true function is more complex. Therefore the statement is true.

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