Main Article Content
Abstract
In this paper, a general base of power transformation under the kernel method is suggested and applied in the line transect sampling to estimate abundance. The suggested estimator performs well at the boundary compared to the classical kernel estimator without using the shoulder condition assumption. The transformed estimator show smaller value of mean squared error and absolute bias from the efficiency results obtained using simulation.
Keywords
line transect
power-transformation
kernel estimator
shoulder condition
abundance
bandwidth
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How to Cite
Albadareen, B. I., & Ismail, N. (2020). A General Base of Power Transformation to Improve the Boundary Effect in Kernel Density without Shoulder Condition. Pakistan Journal of Statistics and Operation Research, 16(2), 279-285. https://doi.org/10.18187/pjsor.v16i2.3164
References
- Al-Bassam, M., & Eidous, O. M. (2018). Combination of parametric and nonparametric estimators for population abundance using line transect sampling. Journal of Information and Optimization Sciences, 39(7), 1449–1462. https://doi.org/10.1080/02522667.2017.1367510
- Albadareen, B., & Ismail, N. (2017). Several new kernel estimators for population abundance. AIP Conference Proceedings, 1830(1), 80018. https://doi.org/10.1063/1.4981002
- Albadareen, B., & Ismail, N. (2018). Adaptive kernel function using line transect sampling. AIP Conference Proceedings, 1940, 020112. https://doi.org/10.1063/1.5028027
- Albadareen, B., & Ismail, N. (2019). An Adaptation of Kernel Density Estimation for Population Abundance using Line Transect Sampling When the Shoulder Condition is Violated. International Journal of Innovative Technology and Exploring Engineering, 9(2), 3494–3498. https://doi.org/10.35940/ijitee.B6582.129219
- Bauer, R. K., Fromentin, J.-M., Demarcq, H., Brisset, B., & Bonhommeau, S. (2015). Co-Occurrence and Habitat Use of Fin Whales, Striped Dolphins and Atlantic Bluefin Tuna in the Northwestern Mediterranean Sea. PLOS ONE, 10(10), e0139218. https://doi.org/10.1371/journal.pone.0139218
- Buckland, S. T. (1985). Perpendicular Distance Models for Line Transect Sampling. Biometrics, 41(1), 177. https://doi.org/10.2307/2530653
- Buckland, Stephen T, Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., & Thomas, L. (2001). Introduction to distance sampling: estimating abundance of biological populations (1st ed.). London: Oxford University Press. Retrieved from https://global.oup.com/academic/product/introduction-to-distance-sampling-9780198509271?q=9780198509271&cc=my&lang=en
- Charpentier, A., & Flachaire, E. (2015). Log-Transform Kernel Density Estimation of Income Distribution. L’Actualité Économique, 91(1–2), 141–159. https://doi.org/10.7202/1036917ar
- Chen, S. X. (1996). A Kernel Estimate for the Density of a Biological Population by Using Line Transect Sampling. Applied Statistics, 45(2), 135. https://doi.org/10.2307/2986150
- Cheng, M. Y., Fan, J., & Marron, J. S. (1997). On automatic boundary corrections. Annals of Statistics, 25(4), 1691–1708. https://doi.org/10.1214/aos/1031594737
- Devroye, L., & Gyorfi, L. (1985). Nonparametric Density Estimation: The L 1 View. Journal of the Royal Statistical Society. Series A (General) (1st ed., Vol. 148). New York: John Wiley and Sons. https://doi.org/10.2307/2981908
- Eberhardt, L. L. (1968). A Preliminary Appraisal of Line Transects. The Journal of Wildlife Management, 32(1), 82. https://doi.org/10.2307/3798239
- Eidous, O. M. (2005). Frequency Histogram Model For Line Transect Data With And Without The Shoulder Condition. Journal of the Korean Statistical Society, 34(1), 49–60. Retrieved from http://www.koreascience.or.kr/article/JAKO200516610508354.page
- Eidous, O. M. (2011a). Additive histogram frequency estimator for wildlife abundance using line transect data without the shoulder condition. Metron, 69(2), 119–128. https://doi.org/10.1007/BF03263552
- Eidous, O. M. (2011b). Variable location kernel method using line transect sampling. Environmetrics, 22(3), 431–440. https://doi.org/10.1002/env.1082
- Eidous, O. M. (2012). A new kernel estimator for abundance using line transect sampling without the shoulder condition. Journal of the Korean Statistical Society, 41(2), 267–275. https://doi.org/10.1016/j.jkss.2011.09.004
- Eidous, O. M. (2015). Nonparametric Estimation of f(0) Applying Line Transect Data with and without the Shoulder Condition. Journal of Information and Optimization Sciences, 36(4), 301–315. https://doi.org/10.1080/02522667.2013.867726
- Eidous, O. M., & Al-Eibood, F. (2018). A bias-corrected histogram estimator for line transect sampling. Communications in Statistics - Theory and Methods, 47(15), 3675–3686. https://doi.org/10.1080/03610926.2017.1361987
- Gates, C. E., Marshall, W. H., & Olson, D. P. (1968). Line Transect Method of Estimating Grouse Population Densities. Biometrics, 24(1), 135. https://doi.org/10.2307/2528465
- Ghosh, S. (2018). Kernel Smoothing: Principles, Methods and Applications (1st ed.). New York: Chapman & Hall. https://doi.org/10.1002/9781118890370
- Jones, M. C., Linton, O., & Nielsen, J. P. (1995). A simple bias reduction method for density estimation. Biometrika, 82(2), 327–338. https://doi.org/10.1093/biomet/82.2.327
- Karunamuni, R. J., & Alberts, T. (2006). A locally adaptive transformation method of boundary correction in kernel density estimation. Journal of Statistical Planning and Inference, 136(9), 2936–2960. https://doi.org/10.1016/j.jspi.2004.12.014
- Koekemoer, G., & Swanepoel, J. W. H. (2008). Transformation Kernel density estimation with applications. Journal of Computational and Graphical Statistics, 17(3), 750–769. https://doi.org/10.1198/106186008X318585
- Mack, Y. P. (2002). Bias-corrected confidence intervals for wildlife abundance estimation. Communications in Statistics - Theory and Methods, 31(7), 1107–1122. https://doi.org/10.1081/STA-120004909
- Mack, Y. P., & Quang, P. X. (1998). Kernel Methods in Line and Point Transect Sampling. Biometrics, 54(2), 606. https://doi.org/10.2307/3109767
- Marron, J. S., & Ruppert, D. (1994). Transformations to Reduce Boundary Bias in Kernel Density Estimation. Journal of the Royal Statistical Society: Series B (Methodological), 56(4), 653–671. https://doi.org/10.1111/j.2517-6161.1994.tb02006.x
- Silverman, B. W. (1986). Density estimation: For statistics and data analysis. Density Estimation: For Statistics and Data Analysis (1st ed.). London: Chapman & Hall. https://doi.org/10.1201/9781315140919
- Wen, K., & Wu, X. (2015). An Improved Transformation-Based Kernel Estimator of Densities on the Unit Interval. Journal of the American Statistical Association, 110(510), 773–783. https://doi.org/10.1080/01621459.2014.969426
- Zhang, S. (2001). Generalized likelihood ratio test for the shoulder condition in line transect sampling. Communications in Statistics - Theory and Methods, 30(11), 2343–2354. https://doi.org/10.1081/STA-100107690