Bias corrected regularization kernel method in ranking

We propose a bias corrected regularization kernel ranking (BCRKR) method and characterize the asymptotic bias and variance of the estimated ranking score function. The results show that BCRKR has smaller asymptotic bias than the traditional regularization kernel ranking (RKR) method. The variance of BCRKR has the same order of decay as that of RKR when the sample size goes to infinity. Therefore, BCRKR is expected to be as effective as RKR and its smaller bias favors its use in block wise data analysis such as distributed learning for big data. The proofs make use of a concentration inequality of integral operator U-statistic.