Nonparametric inference for additive models estimated via simplified smooth backfitting

We investigate hypothesis testing in nonparametric additive models estimated using simplified smooth backfitting (Huang and Yu, Journal of Computational Graphical Statistics, \textbf{28(2)}, 386--400, 2019). Simplified achieves oracle properties under regularity conditions provides closed-form expressions the estimators that are useful for deriving asymptotic properties. develop a generalized likelihood ratio (GLR) loss function (LF) based framework inference. Under null hypothesis, both GLR LF tests have asymptotically rescaled chi-squared distributions, exhibit Wilks phenomenon, which means scaling constants degrees freedom independent nuisance parameters. These optimal terms rates convergence testing. Additionally, bandwidths well-suited model estimation may be show models, test is more powerful than test. use simulations to demonstrate phenomenon power these proposed tests, real example illustrate their usefulness.