The Generalized Poisson Count Technique and its Statistical Inference

WU Qin; LIU Yin; RUAN Jian

doi:10.6054/j.jscnun.2019109

Journal of South China Normal University (Natural Science Edition) > 2019 > 51(6): 107-110. > DOI: 10.6054/j.jscnun.2019109

WU Qin, LIU Yin, RUAN Jian. The Generalized Poisson Count Technique and its Statistical Inference[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(6): 107-110. DOI: 10.6054/j.jscnun.2019109

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The Generalized Poisson Count Technique and its Statistical Inference

WU Qin^1, ,,
LIU Yin²,
RUAN Jian³

1.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
2.
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
3.
Zhongshan Haotou Middle School, Zhongshan 528437, China

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Received Date: January 09, 2019
Available Online: March 21, 2021

Graphical Abstract

Abstract

Abstract

Based on the Generalized Poisson distribution, the Generalized Poisson Count Technique is introduced to solve the over-dispersion and under-dispersion in the Poisson Item Count Technique. For the statistical inference, the iterative algorithm using EM algorithm and MM algorithm is studied to calculate the maximum likelihood estimate in the model by introducing the missing data and constructing the substitution function. Furthermore, in the simulation, the bias of the estimate is presented and the simulation results are discussed to find effective information.
- Generalized Poisson distribution,
- EM algorithm,
- MM algorithm,
- parameter estimation,
- simulation

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References (20)

References

[1]	TANG M L, WU Q, TIAN G L, et al. Two-sample non randomized response techniques for sensitive questions[J]. Communications in Statistics-Theory and Methods, 2014, 43(2):408-425. doi: 10.1080/03610926.2012.657323
[2]	WU Q, TANG M L. Flexible non-randomized response models for survey with sensitive question[J]. Statistics in Medicine, 2014, 33:918-929. doi: 10.1002/sim.5999
[3]	LIU Y, TIAN G L, WU Q, et al. Poisson-Poisson item count techniques for surveys with sensitive discrete quantitative data [J]. Statistical Papers, 2017, 58(1):1-29. doi: 10.1007/s00362-015-0682-2
[4]	TOURANGEAU R, YAN T. Sensitive questions in surveys[J]. Psychological Bulletin, 2007, 133:859-883. doi: 10.1037/0033-2909.133.5.859
[5]	WARNER S L. Randomized response:a survey technique for eliminating evasive answer bias[J]. Journal of the American Statistical Association, 1965, 60:63-69. doi: 10.1080/01621459.1965.10480775
[6]	TIAN G L, YU J W, TANG M L, et al. A new non-randomized model for analyzing sensitive questions with binary outcomes [J]. Statistics in Medicine, 2007, 26:4238-4252. doi: 10.1002/sim.2863
[7]	YU J W, TIAN G L, TANG M L. Two new models for survey sampling with sensitive characteristic:design and ana-lysis[J]. Metrika, 2008, 67:251-263. doi: 10.1007/s00184-007-0131-x
[8]	MILLER J D. A new survey technique for studying deviant behavior[D]. Washington: George Washington University, 1984: 22-24.
[9]	TSUCHIYA T. Domain estimators for the item count technique[J]. Survey Methodoly, 2005, 31:41-51.
[10]	IMAI K. Multivariate regression analysis for the item count technique[J]. Journal of the American Statistical Association, 2011, 106(494):407-416. doi: 10.1198/jasa.2011.ap10415
[11]	PETROCZI A, NEPUSZ T, CROSS P, et al. New non-randomized model to assess the prevalence of discriminating behavior:a pilot study on mephedrone[J]. Substance Abuse Treatment, Prevention, and Policy, 2011, 6:1-20. doi: 10.1186/1747-597X-6-1
[12]	GREENBERG B G, ABUL-ELA A A, SIMMONS W R, et al. The unrelated question randomized response model: theoretical framework[J]. Journal of the American Statistical Association, 1969, 64:520-539. doi: 10.1080/01621459.1969.10500991
[13]	BLAIR G, IMAI K. Statistical analysis of list experiments[J]. Political Analysis, 2012, 20:47-77. doi: 10.1093/pan/mpr048
[14]	TIAN G L, TANG M L, WU Q, et al. Poisson and negative binomial item count techniques for surveys with sensitive question[J]. Statistical Methods in Medical Research, 2017, 26(2):931-947. doi: 10.1177/0962280214563345
[15]	LIU Y, TIAN G L, WU Q, et al. Poisson-Poisson item count techniques for surveys with sensitive discrete quantitative data[J]. Statistical Papers, 2019, 60(5):1763-1791. doi: 10.1007/s00362-017-0895-7
[16]	CONSUL P C. Generalized poisson distributions:properties and applications[M]. New York:CRC Press, 1988.
[17]	何朝兵, 柴士改, 刘华文.截断删失数据下泊松分布参数的点估计[J].华南师范大学学报(自然科学版), 2015, 47(4):141-145. doi: 10.6054/j.jscnun.2015.01.011 HE C B, CHAI S G, LIU H W. Point estimation of parameter of Poisson distribution for truncated and censored data[J]. Journal of South China Normal University(Natural Science Edition), 2015, 47(4):141-145. doi: 10.6054/j.jscnun.2015.01.011
[18]	DEMPSTER A P, LAIRD N M, RUBIN D B. Maximum likelihood from incomplete data via the EM algorithm[J]. Journal of the Royal Statistical Society:Series B, 1977, 39(1):1-38. https://www.researchgate.net/publication/246782707_Maximum_Likelihood_from_Incomplete_Data
[19]	LANGE K. MM optimization algorithms[M]. Los Ange-les, California:SIAM, 2016:93-121.
[20]	SHELDO M R. Simulation[M]. 5th Ed. Los Angeles: Aca-demic Press, 2012.

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