Statistica Sinica 28 (2018), 277-292
Abstract: The constrained partial linear model is fit using a single cone projection, without back-fitting. The cone formulation not only provides efficient computation, but also allows for derivation of convergence rates and inference methods. Conditions for simultaneous root-n convergence of the parameters and optimal convergence for the regression function are given. Hypothesis tests involving the nonlinear regression function, while controlling for the effects of the linear term, use a test statistic whose null distribution is that of a mixture-of-betas random variables, under the normal errors assumption. Inference involving the linear term uses approximate t and F distributions; simulations show these perform well compared to competitors.
Key words and phrases: Constrained estimation, convergence rates, hypothesis testing, isotonic, smoothing.