Principles for Uncertainty Assessment in Kernel Smoothing Estimations

Abstract

In this article, we present application of kernel smoothing estimation and bootstrap on real data. We possess statistically significant data set from experiments performed on composite materials. These data form a random sample of observed variable. Probability distribution function (pdf) of such observed variable is estimated using kernel smoothing approach and bootstrap. This estimation depends on a bandwidth of kernel smoother which is defined using both reference density method and our empirical data. Parameters of typical parametric distributions are also estimated from the same empirical data set. We apply methods such as mean square error (MSE) and integrated square error (ISE) to address the uncertainty and vagueness in pdf estimated by kernel smoothing.