caa a22 4500 477063039 CHVBK 20180405111406.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF00052330 doi (NATIONALLICENCE)springer-10.1007/BF00052330 Limit theorems for the maximum likelihood estimate under general multiply Type II censoring [Elektronische Daten] [Fanhui Kong, Heliang Fei] Assume n items are put on a life-time test, however for various reasons we have only observed the r 1-th,..., r k-th failure times % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaamiEamaaBaaaleaamiaadkhadaWgaaqaaSGaaGymaiaacYcaaWqa% baGaamOBaiaacYcacaGGUaGaaiOlaiaac6caaSqabaGccaGGSaGaam% iEamaaBaaaleaamiaadkhadaWgaaqaaSGaam4AaiaacYcaaWqabaGa% amOBaaWcbeaaaaa!48BB!\[x_{r_{1,} n,...} ,x_{r_{k,} n} \]with % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaaGimaiabgsMiJkaadIhadaWgaaWcbaadcaWGYbWaaSbaaeaaliaa% igdacaGGSaaameqaaiaad6gaaSqabaGccqGHKjYOcqWIVlctcqGHKj% YOcaWG4bWaaSbaaSqaaWGaamOCamaaBaaabaWccaWGRbGaaiilaaad% beaacaWGUbaaleqaaeXatLxBI9gBaGqbaOGae8hpaWJaeyOhIukaaa!521B!\[0 \le x_{r_{1,} n} \le \cdots \le x_{r_{k,} n} > \infty \]. This is a multiply Type II censored sample. A special case where each x ri ,n goes to a particular percentile of the population has been studied by various authors. But for the general situation where the number of gaps as well as the number of unobserved values in some gaps goes to ∞, the asymptotic properties of MLE are still not clear. In this paper, we derive the conditions under which the maximum likelihood estimate of θ is consistent, asymptotically normal and efficient. As examples, we show that Weibull distribution, Gamma and Logistic distributions all satisfy these conditions. The Institute of Statistical Mathematics, 1996 Maximum likelihood estimation nationallicence multiply Type II censoring nationallicence law of large numbers nationallicence central limit theorem nationallicence order statistic nationallicence Kong Fanhui Department of Mathematics and Statistics, University of Maryland Baltimore County, 21228, Baltimore, MD, U.S.A. aut Fei Heliang Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 731-755 0020-3157 48:4<731 1996 48 10463 https://doi.org/10.1007/BF00052330 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00052330 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kong Fanhui Department of Mathematics and Statistics, University of Maryland Baltimore County, 21228, Baltimore, MD, U.S.A aut NATIONALLICENCE 700 1- Fei Heliang Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 731-755 0020-3157 48:4<731 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer