Table of Contents#### Download Safari Books Online apps: Apple iOS | Android | BlackBerry

Entire Site

Free Trial

Safari Books Online is a digital library providing on-demand subscription access to thousands of learning resources.

484 Introduction to Robust Estimation and Hypothesis Testing 10.2 TheilSen Estimator This section describes an estimator first proposed by Theil (1950) and later extended by Sen (1968) that is restricted to the case of a single predictor ( p = 1). Then various extensions to p > 1 are discussed. Temporarily focusing on p = 1, one view of the TheilSen estimator is that it attempts to find a value for the slope that makes Kendall's correlation tau, between y i - bx i and x i , (approximately) equal to zero. This can be seen to be tantamount to the following method. For any i < i , for which x i = x i , let S ii = y i - y i . x i - x i The TheilSen estimate of the slope is b 1ts , the median of all the slopes represented by S ii . The intercept is estimated with M y - b 1 M x , where M y and M x are the usual sample medians of the y and x values, respectively. Sen (1968) derived the asymptotic standard error of the slope estimator, but it plays no role here