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.