Free Trial

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

Share this Page URL

10 Robust Regression > 10.2 Theil-Sen Estimator - Pg. 484

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