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On the relative efficiency of a monotone parameter curve estimator in a functional nonlinear model

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Abstract

Functional regression models that relate functional covariates to a scalar response are becoming more common due to the availability of functional data and computational advances. We introduce a functional nonlinear model with a scalar response where the true parameter curve is monotone. Using the Newton-Raphson method within a backfitting procedure, we discuss a penalized least squares criterion for fitting the functional nonlinear model with the smoothing parameter selected using generalized cross validation. Connections between a nonlinear mixed effects model and our functional nonlinear model are discussed, thereby providing an additional model fitting procedure using restricted maximum likelihood for smoothing parameter selection. Simulated relative efficiency gains provided by a monotone parameter curve estimator relative to an unconstrained parameter curve estimator are presented. In addition, we provide an application of our model with data from ozonesonde measurements of stratospheric ozone in which the measurements are biased as a function of altitude.

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Acknowledgements

We would like to thank the Editor, Associate Editor and two referees for their valuable comments and suggestions that significantly improved the paper. In particular, the comments from one referee led to the simulation based comparison with the smooth-then-monotonize PAV approach extended to the FLM, and expanded literature review. The first author’s research was partially supported by a Graduate Student Central Fellowship from University of California, Santa Barbara.

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Authors and Affiliations

  1. California State University, Bakersfield, USA

    Eduardo L. Montoya

  2. University of California, Santa Barbara, USA

    Wendy Meiring

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  1. Eduardo L. Montoya
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  2. Wendy Meiring
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Correspondence to Eduardo L. Montoya.

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Montoya, E.L., Meiring, W. On the relative efficiency of a monotone parameter curve estimator in a functional nonlinear model. Stat Comput 23, 425–436 (2013). https://doi.org/10.1007/s11222-012-9320-1

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