Abstract
Several information measures and corresponding expressions are presented for progressively censored samples. The discussion includes Fisher information, entropy, Kullback–Leibler information, Pitman closeness, and Tukey's linear sensitivity measure.
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References
Abo-Eleneen ZA (2007) Fisher information and optimal schemes in progressive Type-II censored samples. Model Assist Stat Appl 2:153–163
Abo-Eleneen ZA (2008) Fisher information in type II progressive censored samples. Comm Stat Theory Meth 37:682–691
Abo-Eleneen ZA (2011) The entropy of progressively censored samples. Entropy 13:437–449
Ahmadi J (2007) Some results based on entropy properties of progressive Type-II censored data. J Stat Res Iran 4:191–202
Balakrishnan N, Habibi Rad A, Arghami NR (2007) Testing exponentiality based on Kullback-Leibler information with progressively Type-II censored data. IEEE Trans Reliab 56:301–307
Balakrishnan N, Burkschat M, Cramer E, Hofmann G (2008b) Fisher information based progressive censoring plans. Comput Stat Data Anal 53:366–380
Balakrishnan N, Davies KF, Keating JP (2009a) Pitman closeness of order statistics to population quantiles. Comm Stat Simul Comput 38:802–820
Balakrishnan N, Iliopoulos G, Keating JP, Mason RL (2009b) Pitman closeness of sample median to population median. Stat Probab Lett 79:1759–1766
Balakrishnan N, Davies KF, Keating JP, Mason RL (2010d) Simultaneous closeness among order statistics to population quantiles. J Stat Plan Infer 140:2408–2415
Blyth CR (1972) Some probability paradoxes in choice from among random alternatives: rejoinder. J Am Stat Assoc 67:379–381
Burkschat M, Cramer E (2012) Fisher information in generalized order statistics. Statistics 46:719–743
Chandrasekar B, Balakrishnan N (2002) On a multiparameter version of Tukey’s linear sensitivity measure and its properties. Ann Inst Stat Math 54:796–805
Cover TM, Thomas JA (2006) Elements of information theory, 2nd edn. Wiley, Hoboken
Cramer E, Bagh C (2011) Minimum and maximum information censoring plans in progressive censoring. Comm Stat Theory Meth 40:2511–2527
Cramer E, Ensenbach M (2011) Asymptotically optimal progressive censoring plans based on Fisher information. J Stat Plan Infer 141:1968–1980
Cramer E, Kamps U (2003) Marginal distributions of sequential and generalized order statistics. Metrika 58:293–310
Dahmen K, Burkschat M, Cramer E (2012) A- and D-optimal progressive Type-II censoring designs based on Fisher information. J Stat Comput Simul 82:879–905
Dembo A, Cover TM (1991) Information theoretic inequalities. IEEE Trans Inform Theory 37:1501–1518
Ebrahimi N, Soofi E, Zahedi H (2004) Information properties of order statistics and spacings. IEEE Trans Inform Theory 50:177–183
Efron B, Johnstone IM (1990) Fisher’s information in terms of the hazard rate. Ann Stat 18:38–62
Escobar LA, Meeker WQ (1986) Algorithm AS 218: elements of the Fisher information matrix for the smallest extreme value distribution and censored data. J Roy Stat Soc C (Appl Stat) 35:80–86
Escobar LA, Meeker WQ (2001) The asymptotic equivalence of the Fisher information matrices for type I and type II censored data from location-scale families. Comm Stat Theory Meth 30:2211–2225
Haj Ahmad H, Awad A (2009a) Optimal two-stage progressive censoring with exponential life-times. Dirasat (Science) 36:134–144
Haj Ahmad H, Awad A (2009b) Optimality criterion for progressive Type-II right censoring based on Awad sup-entropy measures. J Stat 16:12–27
Kamps U (1995a) A concept of generalized order statistics. Teubner, Stuttgart
Kamps U (1995b) A concept of generalized order statistics. J Stat Plan Infer 48:1–23
Keating JP, Mason RL, Sen PK (1993) Pitman’s measure of closeness: a comparison of statistical estimators. SIAM, Society for Industrial and Applied Mathematics, Philadelphia
Kullback S (1959) Information theory and statistics. Wiley, New York
Lehmann EL, Casella G (1998) Theory of point estimation, 2nd edn. Springer, New York
Louis TA (1982) Finding the observed information matrix when using the EM algorithm. J Roy Stat Soc Ser B 44:226–233
Nagaraja HN (1994) Tukey’s linear sensitivity and order statistics. Ann Inst Stat Math 46:757–768
Nagaraja HN, Abo-Eleneen ZA (2003) Fisher information in order statistics. Pakistan J Stat 19:161–173
Ng HKT, Chan PS, Balakrishnan N (2002) Estimation of parameters from progressively censored data using EM algorithm. Comput Stat Data Anal 39:371–386
Ng HKT, Chan PS, Balakrishnan N (2004) Optimal progressive censoring plans for the Weibull distribution. Technometrics 46:470–481
Park S (1996) Fisher information in order statistics. J Am Stat Assoc 91:385–390
Park S (2003) On the asymptotic Fisher information in order statistics. Metrika 57:71–80
Park S (2005) Testing exponentiality based on Kullback-Leibler information with the Type-II censored data. IEEE Trans Reliab 54:22–26
Park S (2013) On Kullback-Leibler information of order statistics in terms of the relative risk. Metrika (to appear)
Park S, Zheng G (2004) Equal Fisher information in order statistics. Sankhyā 66:20–34
Park S, Balakrishnan N, Zheng G (2008) Fisher information in hybrid censored data. Stat Probab Lett 78:2781–2786
Park S, Balakrishnan N, Kim SW (2011) Fisher information in progressive hybrid censoring schemes. Statistics 45:623–631
Pitman EJG (1937) The closest estimates of statistical parameters. Math Proc Cambridge Philos Soc 33:212–222
Rad AH, Yousefzadeh F, Balakrishnan N (2011) Goodness-of-fit test based on Kullback-Leibler information for progressively Type-II censored data. IEEE Trans Reliab 60:570–579
Soofi ES (2000) Principal information theoretic approaches. J Am Stat Assoc 95:1349–1353
Tanner MA (1993) Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions, 2nd edn. Springer, New York
Tukey JW (1965) Which part of the sample contains the information? Proc Natl Acad Sci USA 53:127–134
Vajda I (1989) Theory of statistical inference and information. Kluwer Academic Publishers, Dordrecht
Vasicek O (1976) A test for normality based on sample entropy. J Roy Stat Soc Ser B 38: 54–59
Volterman W, Davies KF, Balakrishnan N (2013b) Simultaneous Pitman closeness of progressively Type-II right-censored order statistics to population quantiles. Statistics 47:439–452
Volterman W, Davies KF, Balakrishnan N (2013c) Two-sample Pitman closeness comparison under progressive Type-II censoring. Statistics 47:1305–1320
Wang Y, He S (2005) Fisher information in censored data. Stat Probab Lett 73:199–206
Zheng G, Gastwirth JL (2000) Where is the Fisher information in an ordered sample? Stat Sinica 10:1267–1280
Zheng G, Park S (2004) On the Fisher information in multiply censored and progressively censored data. Comm Stat Theory Meth 33:1821–1835
Zheng G, Park S (2005) Another look at life testing. J Stat Plan Infer 127:103–117
Zheng G, Balakrishnan N, Park S (2009) Fisher information in ordered data: a review. Stat Interface 2:101–113
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Balakrishnan, N., Cramer, E. (2014). Information Measures. In: The Art of Progressive Censoring. Statistics for Industry and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4807-7_9
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DOI: https://doi.org/10.1007/978-0-8176-4807-7_9
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