Global mean sea level (GMSL) has been rising since the last century, posing a serious challenge for the coastal areas. A variety of regression models have been utilized for determining GMSL rise over the past one hundred years, resulting in a large spread of sea level rise rates and multidecadal variations. In this study, we develop a new nonparametric noise model that is data-dependent and considers overfitting due to regression. The noise model is used to determine whether one regression model has significantly better skill than others over the period 1900–2010. The choices of background noise and GMSL reconstruction influence whether two sea level models can be statistically distinguished. With our new nonparametric noise spectra, the differences of model skills in explaining sea level variance are significant only in 34% of model comparisons. However, stepwise trends with three inflection points are significantly more skillful than the linear, quadratic, or exponential trend for most GMSL reconstructions, suggesting the importance of multidecadal variability of sea level rise in the twentieth century. Nevertheless, stepwise trend models cannot be distinguished from models with a long-term harmonic oscillation, indicating that the shape of multidecadal variability is not conclusive. The multidecadal variability is also significant in the steric and barystatic sea level contributions and is related to both natural and anthropogenic forcings. GMSL predictions based on regression fits in the twentieth century underestimate the sea level rise rate over the period 2011–2020 because the sea level acceleration in the recent decade (2011–2020) is not well represented.