Constrained Polynomial Spline Estimation of Monotone Additive Models

• Activity Number: 92
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 9:30 PM to 10:15 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lu Wang* and Lan Xue
• Companies: Oregon State University and Oregon State University
• Keywords: $L_{2}$-norm consistency ; knots ; monotone function estimation ; nonparametric function ; Norwegian farm data ; polynomial spline

Abstract

Monotone additive models are useful in estimating productivity curve or analysis of disease risk where covariates are known to have monotonic effects on the response. Existing literature mainly focuses on univariate monotone smoothing. Available methods for estimation of monotone additive models are either difficult to interpret or have no asymptotic guarantees. In this paper, we propose an one-step backfitted constrained polynomial spline method. It is not only easy to compute by taking numerical advantages of linear programming, but also enjoys the optimal rate of convergence asymptotically. The simulation study and application of our method to Norwegian Farm data suggest that the proposed method has superior performance than the existing ones, especially when the data has outliers.