Nonintrusive load monitoring (NILM) technique tries to measure the power consumption of all appliances at the power meter, the single point where the power cable enters your home. In literature, many algorithms have been proposed to detect appliance usage in smart grid to detect how much and what appliances are in use. In this paper, we emphasis on the issue where the appliance is in use. In practice the signal noise on the power line makes it difficult to differentiate appliances when they are very close. In this paper, we propose a statistical learning based technique that can detect different appliance usage events that occurs very close within just several centimeters. The main idea is to take the sample mean of the appliance readings and apply the hypothesis testing on the sample mean to determine the decision threshold for the classification. Results show that the proposed scheme can achieve centimeter level positioning accuracy.