On Kernel-Based Estimator of Odds Ratio Using Different Stratified Sampling Schemes
Abstract
The kernel-based estimator of Cochran Mantel-Haenszel odds ratio based on stratified simple and ranked set sampling is proposed. The expectation and variance of the estimator are analytically obtained. Using a simulation study, the estimator based on stratified ranked set sampling is more efficient than its counterpart based on stratified simple random sampling. Finally, the estimator's performance is investigated by using base deficit data.References
A. Agresti and M. Kateri. Categorical Data Analysis. Springer, 2011.
M. Al-Odat and M. F. Al-Saleh. A variation of ranked set sampling. Journal of Applied Statistical Science, 10(2):137–146, 2001.
N.Altman and C.Léger. Bandwidth selection for kernel distribution function estimation. Journal of Statistical Planning and Inference, 46(2):195–214, 1995.
A. Azzalini. A note on the estimation of a distribution function and quantiles by a kernel method. Biometrika, 68(1):326–328, 1981.
L. Barabesi and L. Fattorini. Kernel estimators of probability density functions by ranked-set sampling. Communications in Statistics-Theory and Methods, 31(4):597–610, 2002.
L. L. Bohn and D. A. Wolfe. The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analog of the mann-whitney-wilcoxon statistic. Journal of the American Statistical Association, 89(425):168–176, 1994.
Z. Chen. Density estimation using ranked-set sampling data. Environmental and Ecological Statistics, 6(2):135–146, 1999.
Z. Chen, N.-Z. Shi, and W. Gao. Nonparametric estimation of the log odds ratio for sparse data by kernel smoothing. Statistics & Probability Letters, 81(12):1802–1807, 2011.
J. W. Davis, R. C. Mackersie, T. L. Holbrook, and D. B. Hoyt. Base deficit as an indicator of significant abdominal injury. Annals of Emergency Medicine, 20(8):842–844, 1991.
J. W. Davis, S. R. Shackford, R. C. Mackersie, and D. B. Hoyt. Base deficit as a guide to volume resuscitation. The Journal of Trauma, 28(10):1464–1467, 1988.
A. Eftekharian and M. Razmkhah. On estimating the distribution function and odds using ranked set sampling. Statistics & Probability Letters, 122:1–10, 2017.
A. Eftekharian and H. Samawi. On kernel-based quantile estimation using different stratified sampling schemes with optimal allocation. Journal of Statistical Computation and Simulation, 91(5):1040–1056, 2021.
A. Franke and G. Osius. The asymptotic covariance matrix of the odds ratio parameter estimator in semiparametric log-bilinear odds ratio models. Journal of Statistical Planning and Inference, 143(1):63–81, 2013.
J. C. Frey. New imperfect rankings models for ranked set sampling. Journal of Statistical planning and Inference, 137(4):1433–1445, 2007.
Y. Huang, J. Yin, and H. Samawi. Methods improving the estimate of diagnostic odds ratio. Communications in Statistics-Simulation and Computation, 47(2):353–366, 2016.
M. Lejeune and P. Sarda. Smooth estimators of distribution and density functions. Computational Statistics & Data Analysis, 14(4):457–471, 1992.
J. Lim, M. Chen, S. Park, X. Wang, and L. Stokes. Kernel density estimator from ranked set samples. Communications in Statistics-Theory and Methods, 43(10-12):2156–2168, 2014.
I. Locatelli and V. Rousson. Assessing interrater agreement on binary measurements via intraclass odds ratio. Biometrical Journal, 58(4):962–973, 2016.
K.-J. Lui and K.-C. Chang. Notes on odds ratio estimation for a randomized clinical trial with noncompliance and missing outcomes. Journal of Applied Statistics, 37(12):2057–2071, 2010.
V. Mandowara and N. Mehta. Modified ratio estimators using stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 43(3):461–471, 2014.
G. McIntyre. A method for unbiased selective sampling, using ranked sets. Crop and Pasture Science, 3(4):385–390, 1952.
A. Mood, F. Graybill, and D. Boes. Introduction to The Theory of Statistics. McGraw-hill, 1974.
H. Muttlak. Median ranked set sampling. Journal of Applied Statistical Sciences, 6(4):245–255, 1997.
E. A. Nadaraya. Some new estimates for distribution functions. Theory of Probability & Its Applications, 9(3):497–500, 1964.
A. M. Polansky and E. R. Baker. Multistage plug-in bandwidth selection for kernel distribution function estimates. Journal of Statistical Computation and Simulation, 65(1-4):63–80, 2000.
D. Rahardja, H. Wu, S. Huang, and J. Chu. Confidence intervals for the odds ratio of two independent binomial proportions using data with one type of misclassification. Journal of Statistics and Management Systems, 19(2):259–268, 2016.
M. Rosenblatt. Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27(3):832–837, 1956.
H. Samawi, A. Chatterjee, J. Yin, and H. Rochani. On kernel density estimation based on different stratified sampling with optimal allocation. Communications in Statistics-Theory and Methods, 46(22):10973–10990,
H. Samawi, A. Chatterjee, J. Yin, and H. Rochani. On quantiles estimation based on different stratified sampling with optimal allocation. Communications in Statistics-Theory and Methods, 48(6):1529–1544,
H. M. Samawi. Stratified ranked set sample. Pakistan Journal of Statistics-All Series, 12:9–16, 1996.
H. M. Samawi, M. S. Ahmed, and W. Abu-Dayyeh. Estimating the population mean using extreme ranked set sampling. Biometrical Journal, 38(5):577–586, 1996.
H. M. Samawi and M. F. Al-Saleh. Valid estimation of odds ratio using two types of moving extreme ranked set sampling. Journal of the Korean Statistical Society, 42(1):17–24, 2013.
H. M. Samawi and M. I. Siam. Ratio estimation using stratified ranked set sample. Metron, 61(1):75–90, 2003.
S. L. Stokes and T. W. Sager. Characterization of a ranked-set sample with application to estimating distribution
functions. Journal of the American Statistical Association, 83(402):374–381, 1988.
L. N. Tremblay, D. V. Feliciano, G. S. Rozycki, and J. A. Morris Jr. Assessment of initial base deficit as a predictor of outcome: Mechanism of injury does make a difference/discussion. The American surgeon, 68(8):689, 2002.
M. Vock and N. Balakrishnan. A jonckheere–terpstra-type test for perfect ranking in balanced ranked set sampling. Journal of Statistical Planning and Inference, 141(2):624–630, 2011.
W. Wang and G. Shan. Exact confidence intervals for the relative risk and the odds ratio. Biometrics, 71(4):985–995, 2015.
J. Yin, Y. Hao, H. Samawi, and H. Rochani. Rank-based kernel estimation of the area under the roc curve. Statistical Methodology, 32:91–106, 2016.
M. Zhao, Y. Zhao, and I. W. McKeague. Empirical likelihood inference for the odds ratio of two survival functions under right censoring. Statistics & Probability Letters, 107:304–312, 2015.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
