In the literature, the properties and the application of mode estimation is considered under simple random sampling and ranked set sampling (RSS). We investigate some of the asymptotic properties of kernel density-based mode estimation using stratified simple random sampling (SSRS) and stratified ranked set sampling designs (SRSS). We demonstrate that kernel density-based mode estimation using SRSS and SSRS is consistent, asymptotically normally distributed and using SRSS has smaller variance than that under SSRS. Improved performance of the mode estimation using SRSS compared to SSRS is supported through a simulation study. We will illustrate the method by using biomarker data collected in China Health and Nutrition Survey data.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Bellhouse DR, Stafford JE (1999) Density estimation from complex surveys. Stat Sin 9:407–424
Breunig R (2008) Nonparametric density estimation for stratified samples. Stat Probab Lett 78:2194–2200
Buch-Larsen T, Nielsen JP, Guillen M, Bolance C (2005) Kernel density estimation for heavy-tailed distributions using the champernowne transformation. Statistics 39(6):503–518
Chen Z (1999) Density estimation using ranked-set sampling data. Environ Ecol Stat 6(2):135–146
Chen Z (2007) Ranked set sampling: Its essence and new applications. Environ Ecol Stat 14:355–363
Härdle W (2004) Nonparametric and semiparametric models. Springer, Berlin
Hedges SB, Shah P (2003) Comparison of mode estimation methods and application in molecular clock analysis. BMC Bioinform 4(1):31
Jabrah R, Samawi H, Vogel R, Rochani H, Linder D, Klibert J (2017) Using ranked auxiliary covariate as a more efficient sampling design for ANCOVA model: analysis of a psychological intervention to buttress resilience. Commun Stat Appl Methods 24(3):241–257
Jeffrey SS (1996) Smoothing methods in statistics. Springer, New York
Kaur A, Patil G, Sinha A, Taillie C (1995) Ranked set sampling: an annotated bibliography. Environ Ecol Stat 2(1):25–54
Kim J, Scott CD (2012) Robust kernel density estimation. J Mach Learn Res 13:2529–2565
Lim J, Chen M, Park S, Wang X, Stokes L (2014) Kernel density estimator from ranked set samples. Commun Stat-Theory Methods 43:2156–2168
Mahdizadeh M, Zamanzade E (2016) Kernel-based estimation of P(X > Y) in ranked set sampling. Stat Oper Res Trans (SORT) 40(2):243–266
McIntyre GA (1952) A method for unbiased selective sampling, using ranked sets. Aust J Agric Res 3:90–385
Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065–1076
Samawi HM (1996) Stratified ranked set sample. Pak J Stat 12(1):9–16
Samawi HM, Al-Sageer OA (2001) On the estimation of the distribution function using extreme and median ranked set sampling. Biom J 43(3):357–373
Samawi HM, Chatterjee A, Yin J, Rochani H (2017) On kernel density estimation based on different stratified sampling. Commun Stat Theory Methods 46(22):10973–10990
Samawi H, Rochani H, Yin J, Linder D, Vogel R (2018) Notes on kernel density based mode estimation using more efficient sampling designs. Comput Stat 33(2):1071–1090
Silverman BW (1986) Density estimation for statistics and data analysis, vol 26. CRC Press, Boca Raton
Takahasi K, Wakimoto K (1968) On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math 20(1):1–31
Wand M, Jones M (1995) Kernel Smoothing of Monographs on statistics and applied probability, vol 60. Chapman and Hall, London
Yan S, Li J, Li S, Zhang B, Du S, Gordon-Larsen P, Popkin B (2012) The expanding burden of cardiometabolic risk in China: the China Health and Nutrition Survey. Obes Rev 13(9):810–821
The authors thank the associate editor and the reviewers for their valuable comments which improve the manuscript.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Samawi, H., Rochani, H., Yin, J. et al. On Kernel-Based Mode Estimation Using Different Stratified Sampling Designs. J Stat Theory Pract 13, 30 (2019). https://doi.org/10.1007/s42519-018-0034-3
- Mode estimation
- Density kernel estimation
- Stratified ranked set sampling
- Stratified simple random sample
- China health and nutrition survey