Nonparametric Methods in Statistics with SAS Applications

Chapter 7

Univariate Probability Density

Estimation

Let X be a continuous random variable with the probability density function f . Sup-

pose a set of observed realizations of X is available. The objective is to estimate

the density f from the given data set. A parametric approach would be to make an

assumption on the functional form of the density and estimate only the unknown pa-

rameters. If no explicit functional form of f is feasible, a nonparametric approach

steps in. We will study two methods, a histogram, first introduced by Karl Pearson

in 1895,

1

and a kernel estimator attributed to two American statisticians, Murray

Rosenblatt (1926-) and Emanuel ...