Dataset Information

Estimation and model selection for nonparametric function-on-function regression.

ABSTRACT: Regression models with a functional response and functional covariate have received significant attention recently. While various nonparametric and semiparametric models have been developed, there is an urgent need for model selection and diagnostic methods. In this article, we develop a unified framework for estimation and model selection in nonparametric function-on-function regression. We propose a general nonparametric functional regression model with the model space constructed through smoothing spline analysis of variance (SS ANOVA). The proposed model reduces to some of the existing models when selected components in the SS ANOVA decomposition are eliminated. We propose new estimation procedures under either L ₁ or L ₂ penalty and show that the combination of the SS ANOVA decomposition and L ₁ penalty provides powerful tools for model selection and diagnostics. We establish consistency and convergence rates for estimates of the regression function and each component in its decomposition under both the L ₁ and L ₂ penalties. Simulation studies and real examples show that the proposed methods perform well. Technical details and additional simulation results are available in online supplementary materials.

SUBMITTER: Wang Z

PROVIDER: S-EPMC9802009 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Estimation and model selection for nonparametric function-on-function regression.

Wang Zhanfeng Z Dong Hao H Ma Ping P Wang Yuedong Y

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20220328 3

Regression models with a functional response and functional covariate have received significant attention recently. While various nonparametric and semiparametric models have been developed, there is an urgent need for model selection and diagnostic methods. In this article, we develop a unified framework for estimation and model selection in nonparametric function-on-function regression. We propose a general nonparametric functional regression model with the model space constructed through smoo ...[more]

PMID: 36594047

Similar Datasets

Project description:BackgroundThe Brazilian public health system is one of the largest health systems in the world, with a mandate to deliver medical care to more than 200 million Brazilians. The objective of this study is to estimate a production function for primary care in urban Brazil. Our goal is to use flexible estimates to identify heterogeneous returns and complementarities between medical capital and labor.MethodsWe use a large dataset from 2012 to 2016 (with more than 400 million consultations, 270 thousand physicians, and 11 thousand clinics) to nonparametrically estimate a primary care production function and calculate the elasticity of doctors' visits (output) to two inputs: capital stock (number of clinics) and labor (number of physicians). We benchmark our nonparametric estimates against estimates of a Cobb-Douglas (CD) production function. The CD model was chosen as a baseline because it is arguably the most popular parametric production function model. By comparing our nonparametric results with those from the CD model, our paper shed some light on the limitations of the parametric approach, and on the novelty of nonparametric insights.ResultsThe nonparametric results show significantly heterogeneity of returns to both capital and labor, depending on the scale of operation. We find that diseconomies of scale, diminishing returns to scale, and increasing returns to scale are possible, depending on the input range.ConclusionsThe nonparametric model identifies complementarities between capital and labor, which is essential in designing efficient policy interventions. For example, we find that the response of primary care consultations to labor is steeper when capital level is high. This means that, if the goal is to allocate labor to maximize increases in consultations, adding physicians in cities with a high number of clinics is preferred to allocating physicians to low medical infrastructure municipalities. The results highlight how the CD model hides useful policy information by not accounting for the heterogeneity in the data.

Dataset Information

Estimation and model selection for nonparametric function-on-function regression.

Publications

Estimation and model selection for nonparametric function-on-function regression.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets