Estimation of shape constrained additive models with missing response at random

Abstract

Shape constrained additive models are useful in estimating production functions or analysing disease risk where the relationship between predictors and response is known to be monotone or/and concave. We here consider the estimation of shape constrained additive models when the response is missing at random given missing data are common occurrence and problem in many real-life situations. To the best of our knowledge, no research has focused on this problem. Our paper nicely fills this gap and contributes to the literature by proposing a weighted constrained polynomial spline estimation method in a one-step backfitting procedure. The proposed method is not only easy to implement but also gives smooth estimators that satisfy shape constraints and accommodate missing data problem simultaneously. In theory, we show that the proposed estimator enjoys the optimal rate of convergence asymptotically. Both simulation studies and the application of our method to Norwegian farm data illustrate that the proposed method has superior performance due to the incorporation of weights and shape constraints.

Keywords:

• Additive model
• consistency
• missing data
• shape constraint
• polynomial spline

AMS Subject Classifications:

• 62G05
• 62G08

Acknowledgments

The authors thank Dr. Gudbrand Lien for sharing the Norwegian farm data.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the China Postdoctoral Science Foundation [grant number 2019M660272].