Going from Parameter Estimation to Density Estimation

Abstract

A common approach to model variability in integrated circuits is to select a normal distribution for input variables and express variability as a non-linear function of the input variables. Even for simple non-linear functional forms as quadratic polynomials this causes the variability to no longer be normally distributed. It is thus important to be able to estimate the probability distribution of the output. In this chapter we give a brief introduction to the statistical theory of density estimation, which allows to estimate the density of a probability distribution without assuming a specific form of this density. In order to give a self-contained story accessible for non-statisticians, we first present the basic definitions and results of parameter estimation. Then we go beyond parametric estimation by discussing kernel density estimators in detail. We will indicate links with common notions from mathematical analysis such as convolution, Fourier analysis and approximation theory.