Kuan and Lee (2006, Journal of American Statistical Association) proposed a robust M test using the method of Kiefer, Vogelsang, and Bunzel (2000, Econometrica) (referred to as KVB). The test does not require consistent estimation of the asymptotic covariance matrices and is robust not only to heteroscedasticity and serial correlations of unknown form but also to the presence of an estimation effect. However, their proposed test requires recursive estimators that is inefficient for practical implementation and assumes that some matrices are nonsingular. This restricts the application of some classes of the specification test, such as the generalized method of moments (GMM) over-identification test. We therefore propose two KVB-based tests. One is an extension of Newey's (1985, Econometrica) M tests. The other uses orthogonal projection matrices to eliminate estimation effects. The test statistics depend on a full sample estimator and weaken the nonsingular conditions described by Kuan and Lee (2006). Therefore, the test is not only robust but also useful to classes of the specification test on the assumption that the rank of the projection matrix is known a priori. As applications, we consider robust portmanteau tests, GMM over-identification tests and the Hausman tests.