Local asymptotic normality of family of distributions from incomplete observations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 2, pp. 141-154.

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In this paper we prove the property of local asymptotic normality of the likelihood ratio statistics in the competing risks model under random censoring by non-observation intervals.
Keywords: competing risks, random censoring, likelihood ratio, local asymptotic normality.
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Abdurahim A. Abdushukurov; Nargiza S. Nurmuhamedova. Local asymptotic normality of family of distributions from incomplete observations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 2, pp. 141-154. http://geodesic.mathdoc.fr/item/JSFU_2014_7_2_a0/

[1] E. Leman, J. Romano, Testing statistical hypothesis, Springer Verlag, 2008

[2] G. Roussas, Contiguity of Probability Measures: Some Applications in Statistics, University Press, Cambridge, 1972 | MR | Zbl

[3] I. A. Ibragimov, R. Z. Khas'minskii, Asymptotic theory of estimation, Nauka, M., 1979 (in Russian) | MR

[4] J. Hajek, “Local asymptotic minimax and admissibility in estimation”, Proc. Sixth. Berkeley Symp. on Math. Statist. and Prob., v. 1, 1972, 175–194 | MR | Zbl

[5] L. le Cam, “Locally asymptotically normal families of distributions”, Unif. Calif. Publ. Statist., 3 (1960), 37–98 | MR | Zbl

[6] A. A. Abdushukurov, Estimators of unknown distributions from incomplete observations and its properties, LAMBERT Academic Publishing, 2011 (in Russian)

[7] A. A. Abdushukurov, N. S. Nurmuhamedova, “Approximation of the likelihood ratio statistics in competing risks model under random censorship from both sides”, ACTA NUUz, 4 (2011), 162–172 (in Russian)

[8] A. A. Abdushukurov, N. S. Nurmuhamedova, “Asymptotics of the likelihood ratio statistics in competing risks model under multiple right censorship on the right”, Statistical Methods of estimation and Hypothesis Testing, 21, Perm Gos. Univ., Perm, 2012, 4–15 (in Russian)

[9] A. A. Abdushukurov, N. S. Nurmuhamedova, “Local asymptotic normality in the competing risks model”, Uzbekskii Matematicheskii Zhurnal, 2012, no. 2, 5–12 (in Russian)

[10] A. A. Abdushukurov, N. S. Nurmuhamedova, Local asymptotic normality of statical experiments, LAMBERT Academic Publishing, 2012 (in Russian)

[11] A. A. Abdushukurov, N. S. Nurmuhamedova, “Local approximate normality of likelihood ratio statistics in competing risks model under random censorship from both sides”, Far East Journal of Theoretical Statistics, 42:2 (2013), 107–122 | MR | Zbl

[12] M. D. Burke, S. Csörgő, L. Horváth, “Strong approximations of some biometric estimates under random censorship”, Z. Wahrscheinlich. verw. Gebiete, 56 (1981), 87–112 | DOI | MR | Zbl

[13] N. Langberg, F. Proshan, A. J. Quinzi, “Converting dependent models into independents ones, preserving essential features”, Ann. Probab., 6 (1978), 174–181 | DOI | MR | Zbl