  Anomalies are strange data points; they usually represent an unusual
occurrence. Anomaly detection is presented from the perspective of Wireless
sensor networks. Different approaches have been taken in the past, as we will
see, not only to identify outliers, but also to establish the statistical
properties of the different methods. The usual goal is to show that the
approach is asymptotically efficient and that the metric used is unbiased or
maybe biased.
  This project is based on a work done by [1]. The approach is based on the
principle that the entropy of the data is increased when an anomalous data
point is measured. The entropy of the data set is thus to be estimated. In this
report however, preliminary efforts at confirming the results of [1] is
presented. To estimate the entropy of the dataset, since no parametric form is
assumed, the probability density function of the data set is first estimated
using data split method. This estimated pdf value is then plugged-in to the
entropy estimation formula to estimate the entropy of the dataset. The data
(test signal) used in this report is Gaussian distributed with zero mean and
variance 4. Results of pdf estimation using the k-nearest neighbour method
using the entire dataset, and a data-split method are presented and compared
based on how well they approximate the probability density function of a
Gaussian with similar mean and variance. The number of nearest neighbours
chosen for the purpose of this report is 8. This is arbitrary, but is
reasonable since the number of anomalies introduced is expected to be less than
this upon data-split. The data-split method is preferred and rightly so.
