Genotype imputation methods are used to enhance the resolution of genome-wide association studies, and thus increase the detection rate for genetic signals. Although most studies report all univariate summary statistics, many of them limit the access to subject-level genotypes. Because such an access is required by all genotype imputation methods, it is helpful to develop methods that impute summary statistics without going through the interim step of imputing genotypes. Even when subject-level genotypes are available, due to the substantial computational cost of the typical genotype imputation, there is a need for faster imputation methods.