Fast radio bursts (FRBs) are mysterious millisecond-duration radio transients 1, 2. Two possible mechanisms that could generate extremely coherent emission from FRBs invoke neutron star magnetospheres 3-5 or relativistic shocks far from the central energy source 6-8. Detailed polarization observations may help us to understand the emission mechanism. However, the available FRB polarization data have been perplexing, because they show a host of polarimetric properties, including either a constant polarization angle during each burst for some repeaters 9, 10 , or variable polarization angles in some other apparently one-off events 11, 12. Here we report observations of 15 bursts from FRB 180301 and find various polarization

Additive models with backfitting algorithms are popular multivariate nonparametric fitting techniques. However, the inferences of the models have not been very well developed, due partially to the complexity of the backfitting estimators. There are few tools available to answer some important and frequently asked questions, such as whether a specific additive component is significant or admits a certain parametric form. In an attempt to address these issues, we extend the generalized likelihood ratio (GLR) tests to additive models, using the backfitting estimator. We demonstrate that under the null models, the newly proposed GLR statistics follow asymptotically rescaled chi-squared distributions, with the scaling constants and the degrees of freedom independent of the nuisance parameters. This demonstrates that the Wilks phenomenon continues to hold under a variety of smoothing techniques and more relaxed models with unspecified error distributions. We further prove that the GLR tests are asymptotically optimal in terms of rates of convergence for nonparametric hypothesis testing. In addition, for testing a parametric additive model, we propose a bias corrected method to improve the performance of the GLR. The bias-corrected test is shown to share the Wilks type of property. Simulations are conducted to demonstrate the Wilks phenomenon and the power of the proposed tests. A real example is used to illustrate the performance of the testing approach.