There have been recent developments in data-based methods for estimating densities non-parametrically. In this work we shall compare some methods developed by Scott, Duin and Wahba according to their sensitivity, statistical accuracy and cost of implementation when applied to one-dimensional data sets. We shall illustrate the limitations and tradeoffs of each method. The estimates obtained by each method will also be compared to the maximum likelihood univariate Gaussian estimate. We shall also illustrate the application of Duin's method to two-dimensional data sets and compare the results to the maximum likelihood bivariate Gaussian estimate.