Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

3Statistics Basics

Daddy's rifle in my hand felt reassurin', he told me “Red means run, son. Numbers add up to nothin'.” But when the first shot hit the dog, I saw it comin'…

Neil Young (from the song Powderfinger)

In this chapter, we review fundamental methods of statistics.

Most students experience basic statistical estimation by learning, assuming the random outcomes are generated by a familiar distribution (such as the normal). In nonparametric statistics, we may have familiar goals of estimating means and variances, but the applied methods rely less on those underlying assumptions.

We emphasize some statistical methods that are important for nonparametric inference. Specifically, tests and confidence intervals for the binomial parameter are described in detail and serve as building blocks to many nonparametric procedures. The empirical distribution function, a nonparametric estimator for the underlying cumulative distribution, is introduced in the first part of the chapter. We also introduce the likelihood ratio, which is a fundamental statistic for nonparametric inference.

3.1 Estimation

For distributions with unknown parameters (say, ), we form a point estimate as a ...