Contemporary audio declipping algorithms often ignore the possibility of the presence of additive channel noise. If and when noise is present, however, the efficacy of any declipping algorithm is critically dependent on the accuracy with which clipped portions of the signal can be detected. This paper introduces an effective technique for inferring the amplitude and percentile values of the clipping threshold, and develops a statistically-optimal classification algorithm for accurately differentiating between clipped and unclipped samples in a noisy speech signal. The overall effectiveness of the clipped sample estimation algorithm is evaluated by the degree to which automatic speech recognition performance is improved when decoding clipped speech that has been declipped with state-of-the-art declipping algorithms paired with the clipped sample estimation algorithm. Up to 35% relative improvements in word error rate have been observed. Beyond the accuracy of the developed techniques, this paper generally underscores the necessity of robust parameter estimation methods for declipping in noise.