KAJIAN SIMULASI PENDUGAAN SELANG KEPERCAYAAN BOOTSTRAP BAGI ARAH MEDIAN DATA SIRKULAR

  • Cici Suhaeni Institut Pertanian Bogor (IPB)
  • I Made Sumertajaya Institut Pertanian Bogor (IPB)
  • Anik Djuraidah
Keywords: bootstrap confidence interval, circular data, circular statistics, median direction

Abstract

The median direction is one of central tendency of circular data. The estimation process usually requires information about sampling distribution of statistic that want to be used as a parameter estimate. Theoretically, sampling distribution derived from population distribution. But, it is not easy to get sampling distribution of median although the population distribution is known.  When the sampling distribution cannot be derived easily from population distribution, the bootstrap method can be an alternative to handle it. This study wants to evaluate the effect of increasing concentration parameter to the performance of bootstrap confidence interval estimation for median direction through simulation study. Three methods were used to estimate the interval  which are equal-tailed arc (ETA), symmetric arc (SYMA), and likelihood-based arc (LBA). The most important criterion to evaluate them were true coverage and interval width. The simulation results that in general, the increasing of concentration parameter followed by  more narrow interval. For small concentration parameter (k<1), all methods give unstable true coverage and interval width. The authors also identify that those three methods produce intervals with identical width when the parameter concentration is 20 or more. In terms of coverage and interval width, the best method was ETA.

References

Benton, D., & Krishnamoorthy, K. (2002). Performance of the parametric bootstrap method in small sample interval estimates. Advances and Applications in Statistics, 2(3), 269-285.
Casella, G., & Berger, R. L. (2002). Statistical inference (Vol. 2). Pacific Grove, CA: Duxbury.
Ducharme, G. R., Jhun, M., Romano, J. P., & Truong, K. N. (1985). Bootstrap confidence cones for directional data. Biometrika, 72(3), 637-645.
Fisher, N. I., & Hall, P. (1989). Bootstrap confidence regions for directional data. Journal of the American Statistical Association, 84(408), 996-1002.
Fisher, N. I. (1995). Statistical analysis of circular data. Cambridge University Press.

Hall, P. (1988a). On symmetric bootstrap confidence intervals. Journal of the Royal Statistical Society. Series B (Methodological), 50, 35-45.
Hall, P. (1988b). Theoretical comparison of bootstrap confidence intervals. The Annals of Statistics, 16, 927-953.
Jammalamadaka, S. R., & Sengupta, A. (2001). Topics in circular statistics (Vol. 5). World Scientific.
[Kemenkes] Pusat Data dan Surveilans Epidemiologi Kementrian Kesehatan RI. (2010). Demam berdarah dengue di Indonesia tahun 1968-2009. Buletin jendela epidemiologi, 2, 1-14.
Moore, D. S., & McCabe, G. P. (1998). Introduction to the Practice of Statistics, Third edition. W.H. Freeman and Company
Otieno, B. S. (2002). An alternative estimate of preferred direction for circular data (Doctoral dissertation, Virginia Tech).
Rice, J. (2006). Mathematical statistics and data analysis. Nelson Education.
Suhaeni, C., Sumertajaya, I. M., & Djuraidah, A. (2012). Pendugaan Selang Kepercayaan Bootstrap bagi Arah Rata-rata Data Sirkular. Forum Statistika dan Komputasi, 17(2), 1-8.
Published
2018-04-30
Section
Articles