One of the key parameters in density and regression estimation is the bandwidth. This has variously been termed as kernel width or window by various authors. It is a smoothing parameter that determines the amount of data that falls within it and therefore the amount of information that will be used to do the estimation. Under ideal situations it would be expected that there would be a bandwidth selector that does result in estimates with huge biases or variances. Unfortunately this is not the case as small bandwidths reduce the bias at the expense of huge variance while large ones has a desirable variance but unacceptably high bias. This study explores this important parameter, its optimality and influence on density and regression estimation techniques.
Keywords: bias-variance trade-off., kernel function, mean integrated square error
