Hengfang Wang / Abstract: Calibration estimation is widely used when researchers want to estimate the population mean with the adjustment of the survey weights when auxiliary variables are available. However, before such calibration estimation, several functions for calibration equations have to be determined. In this talk, we employ a reproducing kernel Hilbert space to do the approximation between sample space and population space of covariate to get such adjustment of survey weights without predetermining functions. In addition, such infinite-dimensional approximation problem has a finite-dimensional representation when we do the optimizations. The convergence rate of our proposed estimator has been studied. Numerical experiments have been done to illustrate the performance of our proposed estimator.