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Abstract:
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In monthly death counts, the strong seasonal patterns and the strength of such patterns varies over both year and age. A structure like this lends itself to varying-coefficient surfaces modulating the coefficients of (co)sine regressors. Yet, such modulation models can be too simplistic: they cannot handle sharp peaks in the winter. We rather assume a general carrier wave, modulated over time and age, an unknown period twelve vector. This leads to a bilinear model:(1) For a fixed carrier wave, we have a varying-coefficient surface model, estimated with tensor-product P-splines. (2) For fixed varying coefficients, we estimate the carrier wave using generalized linear regression. Penalties are attached on both the row and columns of tensor product coefficients; tuning is optimized with QIC. Efficient computation can be achieved using array regression, with female respiratory death example.
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