Location and Scale Estimation with Correlation Coefficients |
| |
Authors: | Rudy Gideon Adele Marie Rothan |
| |
Institution: | 1. Emeritus, Department of Mathematical Sciences , University of Montana , Missoula , Montana , USA GideonR@mso.umt.edu;3. Department of Mathematical Sciences and Physics , St. Catherine University , St. Paul , Minnesota , USA |
| |
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 |
|
|