Zhang, Haixiang; Wang, Dehui; Zhu, Fukang The empirical likelihood for first-order random coefficient integer-valued autoregressive processes. (English) Zbl 1208.62143 Commun. Stat., Theory Methods 40, No. 3, 492-509 (2011). Summary: This article studies the empirical likelihood method for the first-order random coefficient integer-valued autoregressive process. The limiting distribution of the log empirical likelihood ratio statistic is established. Confidence region for the parameter of interest and its coverage probabilities are given, and hypothesis testing is considered. The maximum empirical likelihood estimator for the parameter is derived and its asymptotic properties are established. The performances of the estimator are compared with the conditional least squares estimator via simulation. Cited in 25 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62G15 Nonparametric tolerance and confidence regions 62F10 Point estimation 62F03 Parametric hypothesis testing Keywords:asymptotic distribution; conditional least squares; hypothesis testing; INAR model; maximum empirical likelihood PDFBibTeX XMLCite \textit{H. Zhang} et al., Commun. Stat., Theory Methods 40, No. 3, 492--509 (2011; Zbl 1208.62143) Full Text: DOI References: [1] DOI: 10.1080/03610929208830925 · Zbl 0775.62225 · doi:10.1080/03610929208830925 [2] DOI: 10.1111/j.1467-9892.1987.tb00438.x · Zbl 0617.62096 · doi:10.1111/j.1467-9892.1987.tb00438.x [3] DOI: 10.1111/j.1467-9574.1988.tb01521.x · Zbl 0647.62086 · doi:10.1111/j.1467-9574.1988.tb01521.x [4] Billingsley P., Statistical Inference for Markov Process (1961) · Zbl 0106.34201 [5] Chan N. H., Econometric Theor. 22 pp 403– (2006) [6] DOI: 10.1016/j.jeconom.2006.12.002 · Zbl 1418.62191 · doi:10.1016/j.jeconom.2006.12.002 [7] DOI: 10.1111/1467-9868.00408 · Zbl 1063.62064 · doi:10.1111/1467-9868.00408 [8] Chuang C. S., Statistica Sinica 12 pp 387– (2002) [9] Hall P., Martingale Limit Theory and Its Application (1980) · Zbl 0462.60045 [10] DOI: 10.1214/aos/1069362388 · Zbl 0881.62095 · doi:10.1214/aos/1069362388 [11] DOI: 10.2307/1427362 · Zbl 0664.62089 · doi:10.2307/1427362 [12] DOI: 10.1093/biomet/84.2.395 · Zbl 0882.62082 · doi:10.1093/biomet/84.2.395 [13] DOI: 10.1214/aos/1176324527 · Zbl 0877.62004 · doi:10.1214/aos/1176324527 [14] DOI: 10.1093/biomet/75.2.237 · Zbl 0641.62032 · doi:10.1093/biomet/75.2.237 [15] DOI: 10.1214/aos/1176347494 · Zbl 0712.62040 · doi:10.1214/aos/1176347494 [16] DOI: 10.1214/aos/1176348368 · Zbl 0799.62048 · doi:10.1214/aos/1176348368 [17] DOI: 10.1214/aos/1176325370 · Zbl 0799.62049 · doi:10.1214/aos/1176325370 [18] DOI: 10.1214/aop/1176994950 · Zbl 0418.60020 · doi:10.1214/aop/1176994950 [19] DOI: 10.1111/j.1467-9892.2006.00472.x · Zbl 1126.62086 · doi:10.1111/j.1467-9892.2006.00472.x [20] DOI: 10.1016/j.jspi.2005.12.003 · Zbl 1098.62117 · doi:10.1016/j.jspi.2005.12.003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.