Statistica Sinica 28 (2018), 277-292

CONSTRAINED PARTIAL LINEAR

REGRESSION SPLINES

Mary C. Meyer

Colorado State University

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.