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## Imputation-based semiparametric estimation for INAR(1) processes with missing data

#### Wei XİONG [1] , Dehui WANG [2] , Xinyang WANG [3]

In applied problems parameter estimation with missing data has risen as a hot topic. Imputation for ignorable incomplete data is one of the most popular methods in integer-valued time series. For data missing not at random (MNAR), estimators directly derived by imputation will lead results that is sensitive to the failure of the effectiveness. In view of the first-order integer-valued autoregressive (INAR(1)) processes with MNAR response mechanism, we consider an imputation based semiparametric method, which recommends the complete auxiliary variable of Yule-Walker equation. Asymptotic properties of relevant estimators are also derived. Some simulation studies are conducted to verify the effectiveness of our estimators, and a real example is also presented as an illustration.
integer-valued autoregressive, semiparametric likelihood, first-step imputation, missing not at random
• [1] M.A. Al-Osh and A.A. Alzaid, First-order integer-valued autoregressive (INAR(1)) process, J. Time Series Anal. 8 (3), 261–275, 1987.
• [2] J. Andersson and D. Karlis, Treating missing values in INAR(1) models: an application to syndromic surveillance data, J. Time Series Anal. 31 (1), 12-19, 2010.
• [3] I.V. Basawa, P.D. Feigin and C.C. Heyde, Asymptotic properties of maximum likelihood estimators for stochastic processes, Sankhya A 38 (3), 259-270, 1976.
• [4] X. Chen, A.T.K.Wan and Y. Zhou, Efficient quantile regression analysis with missing observations, J. Amer. Statist. Assoc. 110, 723-741, 2015.
• [5] X. Cui, J. Guo and G. Yang, On the identifiability and estimation of generalized linear models with parametric nonignorable missing data mechanism, Comput. Statist. Data Anal. 107, 64-80, 2017.
• [6] J. Du and Y. Li, The integer-valued autoregressive (INAR(p)) model, J. Time Series Anal. 12 (2), 129-142, 1991.
• [7] R.K. Freeland and B.P.M. Mccabe, Analysis of low count time series data by poisson autoregression, J. Time Series Anal. 25 (5), 701-722, 2004.
• [8] P. Hall and C.C. Heyde, Martingale Limit Theory and Its Application, Academic Press, New York, 1980.
• [9] M.A. Jazi, G. Jones, and C.D. Lai, Integer valued AR(1) with geometric innovations, J. Iran. Stat. Soc. (JIRSS) 2 (2), 173-190, 2012.
• [10] B. Jia, D. Wang and H. Zhang, A study for missing values in PINAR(1)T processes, Comm. Statist. Theory Methods 43 (22), 4780-4789, 2014.
• [11] R. Jung, G. Ronning and A. Tremayne, Estimation in conditional first order autoregression with discrete support, Statist. Papers 46 (2), 195-224, 2005.
• [12] S.A. Khashimov, The central limit theorem for generalized U-statistics for weakly dependent vectors, Theory Probab. Appl. 38 (3), 563-578, 1993.
• [13] J.K. Kim and C.L. Yu, A semiparametric estimation of mean functionals with nonignorable missing data, J. Amer. Statist. Assoc. 106 (493), 157-165, 2012.
• [14] J.K. Kim and J. Shao, Statistical Methods for Handling Incomplete Data, CRC Press, Boco Raton, 2013.
• [15] R.J.A. Little and D.B. Rubin, Statistical Analysis with Missing Data, Second Edition, John Wiley & Sons, 2002.
• [16] T.A. Louis, Finding the observed information matrix when using the EM algorithm, J. R. Stat. Soc. Ser. B. Stat. Methodol. 44, 226-233, 1982.
• [17] K. Morikawa, J.K. Kim and Y. Kano, Semiparametric maximum likelihood estimation with data missing not at random, Canad. J. Statist. 45 (4), 393-409, 2017.
• [18] W.K. Newey and D.L. McFadden, Large sample estimation and hypothesis testing, in: Handbook of Econometrics, Vol. IV , Engle R.F., McFadden D.L. editors, North Holland, Amsterdam, 1994.
• [19] M. Pourahmadi, Estimation and interpolation of missing values of a stationary time series, J. Time Series Anal. 10 (2), 149-169, 1989.
• [20] M.K. Riddles, J.K. Kim and J. Im, Propensity-score-adjustment method for nonignorable nonresponse, Journal of Survey Statistics and Methodology 4, 215-245, 2016.
• [21] D.B. Rubin, Inference and missing data, Biometrika 63 (3), 581-592, 1976.
• [22] J. Shao and L. Wang, Semiparametric inverse propensity weighting for nonignorable missing data, Biometrika 103, 175-187, 2016.
• [23] N. Tang, P. Zhao and H. Zhu, Empirical likelihood for estimating equations with nonignorably missing data, Statist. Sinica 24, 723-747, 2014.
• [24] S. Wang, J. Shao and J.K. Kim, An instrumental variable approach for identification and estimation with nonignorable nonresponse, Statist. Sinica 24, 1097-1116, 2014.
• [25] K. Yang, D.Wang, B. Jia and H. Li, An integer-valued threshold autoregressive process based on negative binomial thinning, Statist. Papers 59 (3), 1131-1160, 2018.
• [26] H. Zhang, D. Wang and F. Zhu, Inference for INAR(p) processes with signed generalized power series thinning operator, J. Statist. Plann. Inference 140 (3), 667-683, 2010.
• [27] H. Zheng, I.V. Basawa and S. Datta, Inference for pth-order random coefficient integer-valued autoregressive processes, J. Time Series Anal. 27 (3), 411-440, 2006.
Primary Language en Statistics and Probability Statistics Orcid: 0000-0002-0864-5183Author: Wei XİONG Institution: Jilin UniversityCountry: China Orcid: 0000-0002-9185-9034Author: Dehui WANG (Primary Author)Institution: Jilin UniversityCountry: China Orcid: 0000-0001-5460-5281Author: Xinyang WANG Institution: Shenyang Normal UniversityCountry: China National Natural Science Foundation of China, Natural Science Foundation of Jilin Province, Program for Changbaishan Scholars of Jilin Province, Science and Technology Program of Jilin Educational Department during the “13th Five-Year” Plan Period No. 11731015, 11571051, 11501241, 11871028, No. 20150520053JH, 20170101057JC, 20180101216JC, 2015010, No. 2016316 Publication Date : October 6, 2020
 Bibtex @research article { hujms643081, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1843 - 1864}, doi = {10.15672/hujms.643081}, title = {Imputation-based semiparametric estimation for INAR(1) processes with missing data}, key = {cite}, author = {Xi̇ong, Wei and Wang, Dehui and Wang, Xinyang} } APA Xi̇ong, W , Wang, D , Wang, X . (2020). Imputation-based semiparametric estimation for INAR(1) processes with missing data . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1843-1864 . DOI: 10.15672/hujms.643081 MLA Xi̇ong, W , Wang, D , Wang, X . "Imputation-based semiparametric estimation for INAR(1) processes with missing data" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1843-1864 Chicago Xi̇ong, W , Wang, D , Wang, X . "Imputation-based semiparametric estimation for INAR(1) processes with missing data". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1843-1864 RIS TY - JOUR T1 - Imputation-based semiparametric estimation for INAR(1) processes with missing data AU - Wei Xi̇ong , Dehui Wang , Xinyang Wang Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.643081 DO - 10.15672/hujms.643081 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1843 EP - 1864 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.643081 UR - https://doi.org/10.15672/hujms.643081 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Imputation-based semiparametric estimation for INAR(1) processes with missing data %A Wei Xi̇ong , Dehui Wang , Xinyang Wang %T Imputation-based semiparametric estimation for INAR(1) processes with missing data %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.643081 %U 10.15672/hujms.643081 ISNAD Xi̇ong, Wei , Wang, Dehui , Wang, Xinyang . "Imputation-based semiparametric estimation for INAR(1) processes with missing data". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1843-1864 . https://doi.org/10.15672/hujms.643081 AMA Xi̇ong W , Wang D , Wang X . Imputation-based semiparametric estimation for INAR(1) processes with missing data. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1843-1864. Vancouver Xi̇ong W , Wang D , Wang X . Imputation-based semiparametric estimation for INAR(1) processes with missing data. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1843-1864.

Authors of the Article
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