A New Estimator of a Circular Median

Abstract

It is well known that for distributions on the real line, the variability of sample median as an estimator of the population median remains almost the same when the sample of size 2k increases by 1 (2k + 1). Quasi medians—the averages of two symmetrically placed order statistics—were introduced by Hodges and Lehmann (1967) as alternative estimators of the location parameter, reducing the variability of the estimator in the case of samples with odd sizes. This article explores the analogous idea for the data on the circle. We propose the CQM—a circular mean of the two most central order statistics on a circle—as the estimator of a population median. The proposed estimator improves the well known Mardia median (Mardia, 1972) when the sample size is odd, and coincides with it when the sample size is even.

Keywords:

• Circular median
• Mardia median
• New median
• Quasi median

Mathematics Subject Classification:

• 62H11
• 62F10