IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
Lee-Carter parameters are fitted by singular value decomposition (SVD) of the matrix of centred log rates. Which statement about this approach is correct?
The first singular vectors, after normalisation, give b(x) and k(t), and this is the best rank-one least-squares approximation to the centred log mortality matrix. a(x) is obtained by averaging beforehand, and the method is not a Poisson likelihood fit.
- AThe first singular vectors give b(x) and k(t) up to normalisation, and the fit is the best rank-one approximation in least squaresCorrect
- BIt assumes the errors are Poisson distributed and maximises the Poisson likelihood exactly
- CThe second singular vectors are used for b(x) and k(t) because the first represents a(x)
- DIt requires k(t) to be stationary before the SVD is applied
- It produces a(x) as the first singular vector
Explanation
Subtract a(x), the row average of log m, then SVD of the residual matrix. The leading singular vectors give the best rank-one least-squares approximation, which are rescaled to b and k. Poisson likelihood is a different fitting method, and a(x) comes from averaging, not SVD.
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