Document Type

Article

Publication Title

Communications in Statistics - Theory and Methods

Publication Date

2-2011

Volume

40

Issue

9

Disciplines

Mathematics

Abstract

This article shows how to use any correlation coefficient to produce an estimate of location and scale. It is part of a broader system, called a correlation estimation system (CES), that uses correlation coefficients as the starting point for estimations. The method is illustrated using the well-known normal distribution. This article shows that any correlation coefficient can be used to fit a simple linear regression line to bivariate data and then the slope and intercept are estimates of standard deviation and location. Because a robust correlation will produce robust estimates, this CES can be recommended as a tool for everyday data analysis. Simulations indicate that the median with this method using a robust correlation coefficient appears to be nearly as efficient as the mean with good data and much better if there are a few errant data points. Hypothesis testing and confidence intervals are discussed for the scale parameter; both normal and Cauchy distributions are covered.

Keywords

Confidence intervals; Hypothesis testing; Robust estimates; Simple linear regression

DOI

10.1080/03610921003694430

Rights

© 2011 Taylor & Francis Group, LLC

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