Change detection in streaming data relies on a fast estimation of the probability that the data in two consecutive windows come from different distributions. Choosing the criterion is one of the multitude of questions that need to be addressed when designing a change detection procedure. This paper gives a log-likelihood justification for two well-known criteria for detecting change in streaming multidimensional data: Kullback-Leibler (K-L) distance and Hotelling's T-square test for equal means (H). We propose a semiparametric log-likelihood criterion (SPLL) for change detection. Compared to the existing log-likelihood change detectors, SPLL trades some theoretical rigor for computation simplicity. We examine SPLL together with K-L and H on detecting induced change on 30 real data sets. The criteria were compared using the area under the respective Receiver Operating Characteristic (ROC) curve (AUC). SPLL was found to be on the par with H and better than K-L for the nonnormalized data, and better than both on the normalized data.