Bootstrap Confidence Interval Estimation of Preferred Direction for Circular Data

Abstract

The confidence interval is an estimator based on the sampling distribution. When the sampling distribution can not be derived from population distribution, the bootstrap method can be used to estimate it. Three methods used to estimate the bootstrap confidence interval for circular data were equal-tailed arc (ETA), symmetric arc (SYMA), and likelihood-based arc (LBA). In this study, three methods were evaluated through simulation study. The most important criterion to evaluate them were true coverage and interval width. The simulation results indicated in all methods, the interval width shortened when the concentration parameter increased. True coverage approached confidence level when the concentration parameter were one or more. For small concentration parameter, all three methods appeared unstable. Based on the true coverage, SYMA was the best, while in terms the interval width, LBA was the best one. For both criterion could be summarized that ETA is the best result. ETA and SYMA applicated for estimate the period of Dengue Fever outbreaks in Bengkulu. The estimation showed that Dengue Fever outbreaks in 2009 were October through January. In 2010, it were January through March, and in 2011, it were June through September.