CHOICE OF SMOOTHING PARAMETER IN KERNEL DENSITY ESTIMATION

ABSTRACT

The problem is we may not know the probability distribution for a random variable. We rarely do know the distribution because we don’t have access to all possible outcomes for a random variable. In fact, all we have access to be a sample of observations. As such, we must select a probability distribution. This problem is referred to as probability density estimation, or simply “density estimation,” as we are using the observations in a random sample to estimate the general density of probabilities beyond just the sample of data we have available

We have described density estimation using the selected choice of the smoothing parameter, one of the parameter in density and regression estimation is bandwidth.. In this study we had our focus on the univariate dataset excluding the multivariate cases. We also derived the approximated MISE (bias² + Var.) so as to identify the optimal bandwidth.

Bandwidth here acts as a smoothing parameter, controlling the tradeoff between bias and variance in the result. This work is based on 3 methods (Silverman’s rule of thumb, the subjective method, the plug in method) of selecting bandwidth.