Multivariate spline analysis for multiplicative models: Estimation, testing and application to climate change

With regard to hypothesis testing, we focus on the “no effect” test and prove that the null distribution of the penalized likelihood ratio test (PLRT) does not depend on the nuisance parameters under H0, leading to easy Monte-Carlo techniques. Numerical results are presented for both simulated data and climate data. For simulated data, our estimation algorithm is shown to have a good behavior. The application to climate data illustrates how multivariate spline analysis for multiplicative models may be of interest in climate change detection.