Optimal design for adaptive smoothing splines. We consider the design problem of collecting temporal/longitudinal data. The adaptive smoothing spline is used as the analysis model where the prior curvature information can be naturally incorporated as a weighted smoothness penalty. The estimator of the curve is expressed in linear mixed model form, and the information matrix of the parameters is derived. The D-optimality criterion is then used to compute the optimal design points. An extension is considered, for the case where subpopulations exert different prior curvature patterns. We compare properties of the optimal designs with the uniform design using simulated data and apply our method to the Berkeley growth data to estimate the optimal ages to measure heights for males and females. The approach is implemented in an R package called “ODsplines”, which is available from github.com/jialiwang1211/ODsplines.

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