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ABSTRACT
In this project we focused on the topic of kernel density estimation, where we extensively covered the use of the Gaussian kernel and a selected smoothing parameter. In addition, we explored two different approaches to density estimation: parametric and non-parametric. To support our discussion, we conducted an in-depth review of literature done by various scholars on density estimation, kernel density estimation, and bandwidth selection. We investigated different methods for bandwidth selection, including the subjective choice of bandwidth, Silverman's rules of thumb, the least square cross-validation method, the maximum likelihood cross-validation method, and the plug-in method. We also derived the approximated mean integrated squared error (MISE), which is the sum of the bias square and variance. We concluded that although there is no universally accepted method of choosing the smoothing parameter, Silverman's rule of thumb performed better than the other methods we used.
