Joint estimation of monotone curves via functional principal component analysis

A functional data approach is developed to jointly estimate a collection of monotone curves that are irregularly and possibly sparsely observed with noise. In this approach, the unconstrained relative curvature curves instead of the monotone-constrained functions are directly modeled. Functional principal components are used to describe the major modes of variations of curves and allow borrowing strength across curves for improved estimation. A two-step approach and an integrated approach are considered for model fitting. The simulation study shows that the integrated approach is more efficient than separate curve estimation and the two-step approach. The integrated approach also provides more interpretable principle component functions in an application of estimating weekly wind power curves of a wind turbine. (C) 2021 Published by Elsevier B.V.

Automated summary

A functional data approach is developed to estimate a collection of monotone curves that are irregularly and possibly sparsely observed with noise. Unconstrained relative curvature curves are directly modeled, with functional principal components used to describe major modes of curve variations for improved estimation. Two model fitting approaches are considered, with the integrated approach shown to be more efficient than separate curve estimation and the two-step approach.