ESTIMATION OF TRIGONOMETRIC MOMENTS FOR CIRCULAR DISTRIBUTION OF MA(p)TYPE BY USING BINARY SERIES

Abstract

Directional statistics have received a great deal of interest in recent years, and a variety of distributions on the circle have been proposed. In this paper, we propose circular distributions of a moving average model of order p type which includes the cardioid distribution, and discuss estimation of trigonometric moments based on binary series. We give an explicit form of the root n consistent estimator based on clipped series, which enables us to construct an efficient estimator by the Newton– Raphson iterative method. We also show a robustness of the proposed estimator when the probability density function is contaminated with a noise term.