Journal of the American Statistical Association · 1968 · 1.7K citations · 0 references
Natural SciencesBiostatisticsEconometricsStatistical ModelingStatisticsEstimation TheoryInferential StatisticsNonparametric StatisticsOrder StatisticsRobust StatisticsStatistical AnalysisConfidence Interval EstimationConfidence Interval EvaluationConfidence Intervals For Regression CoefficientsNonparametric Confidence IntervalsRank-order CorrelationRobust Confidence IntervalsRobust Correlation EstimationSpearman Rank Correlation Coefficient
The least squares estimator of a regression coefficient β is vulnerable to gross errors and its confidence interval is sensitive to non-normality. This paper investigates a simple, robust estimator of β based on Kendall’s rank correlation tau. The estimator is the median of all pairwise slopes, is unbiased, and its confidence interval is derived from two order statistics of these slopes, with properties compared to least squares and other nonparametric estimators.
Abstract The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence interval is also determined by two order statistics of this set of slopes. Various properties of these estimators are studied and compared with those of the least squares and some other nonparametric estimators.