Constrained polynomial spline estimation of monotone additive models

• Efficient estimation of monotone additive models.
• One-step backfitted constrained polynomial spline method.
• Easy to compute with only linear constrains.
• Robust to outliers and better numerical performance.
• Enjoys optimal L2L2 rate of convergence asymptotically.

Monotone additive models are useful in estimating productivity curve or analyzing disease risk where the predictors 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 a one-step backfitted constrained polynomial spline method for monotone additive models. 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.