A naive likelihood ratio (LR) estimation using the observed frequencies of events can overestimate LRs for infrequent data. One approach to avoid this problem is to use a frequency threshold and set the estimates to zero for frequencies below the threshold. This approach eliminates the computation of some estimates, thereby making practical tasks using LRs more efficient. However, it still overestimates LRs for low frequencies near the threshold. This study proposes a conservative estimator for low frequencies, slightly above the threshold. Our experiment used LRs to predict the occurrence contexts of named entities from a corpus. The experimental results demonstrate that our estimator improves the prediction accuracy while maintaining efficiency in the context prediction task.