Preview

Industrial laboratory. Diagnostics of materials

Advanced search
Open Access Open Access  Restricted Access Subscription Access

Fisher information in a competing risks model with inhomogeneous random interval censoring

https://doi.org/10.26896/1028-6861-2025-91-7-85-93

Abstract

Fisher information is a fundamental concept in the theory of statistical inference and plays a crucial role in the estimation of parameters in statistical models. It represents a measure of the informativeness of observed data with respect to the unknown parameters of the model. In situations involving random censoring, where some observations may be incomplete or censored, calculating Fisher information becomes a complex task that has garnered significant attention from researchers. In this paper, we compute and investigate the Fisher information in a competing risks model under inhomogeneous random interval censoring. The results obtained indicate that under certain conditions, Fisher information retains its properties even in the presence of incomplete observations, which is crucial for improving the accuracy of parameter estimation in statistical models.

About the Author

Nargiza S. Nurmukhamedova
National University of Uzbekistan named after Mirzo Ulugbek
Uzbekistan

Nargiza S. Nurmukhamedova,

4, Universitetskaya ul., Tashkent, 100174.



References

1. Fisher R. A. Theory of Statistical Estimation / Proceedings of the Cambridge Philosophical Society. 1925. P. 700 – 725.

2. Zacks Sh. The theory of statistical inference. — New York: Wiley, 1971. — 609 p.

3. Efron B., Zonstone I. M. Fisher Information in terms of the hazard rate / Ann. Statistics 1990. Vol. 18. No. 1. P. 38 – 62.

4. Prakasa Rao B. L. S. On Cramer – Rao type integral inequalities / Calcutta Stat. Assoc. Bull. 1991. Vol. 40. P. 183 – 205.

5. Prakasa Rao B. L. S. Cramer – Rao type integral inequalities for functions of multidimensional parameter / Sankhya: Ser. A. 1992. Vol. 54. P. 53.

6. Prakasa Rao B. L. S. Improved Cramer – Rao type integral inequalities or Bayesian Cramer – Rao lower-band / J. Indian Soc. Probabil. Stat. 2018. Vol. 19. P. 1 – 7.

7. Prakasa Rao B. L. S. Improved sequential Cramer – Rao type integral inequality / Sequential Analysis. 2018. Vol. 37. P. 59 – 68.

8. Abdushukurov A. A., Kim L. V. Lower Cramer – Rao and Bhattacharyya bunds for randomly censored observation / J. Soviet. Math. 1987. Vol. 38. No. 5. P. 2171 – 2185.

9. Prakasa Rao B. L. S. Remarks on Cramer – Rao type integral inequalities for random censored data / Anal. Cens. Data. 1995. Vol. 27. P. 163 – 175.

10. Zheng G., Gastwirth J. H. On the Fisher information in randomly censored data / Stat. Probabil. Lett. 2001. Vol. 52. P. 421 – 426.

11. Zeng G., Gastwirth J. H. Fisher information in ordered randomly censored data with application to characterization problems / Stat. Sinica. 2003. Vol. 13. P. 507 – 517.

12. Prakasa Rao B. L. S. Improved Cramer – Rao inequality for randomly censored data / J. Iran. Stat. Soc. 2018. Vol. 17. P. 17 – 26.

13. Prakasa Rao B. L. S. Cramer – Rao Inequality Revisited for Randomly Censored Data / Proc. of the Conf. «Statistics and its applications». 2019. Tashkent. P. 19 – 28.

14. Abdushukurov A., Nurmukhamedova N. Locally asymptotically normality of the family of distributions by incomplete observations / J. Sib. Fed. Univ. Math. Phys. 2014. Vol. 7. P. 141 – 154.

15. Abdushukurov A., Nurmukhamedova N. Asymptotic properties of Bayesian-type estimates in the competing risks model under random censoring / J. Math. Sci. (U.S.). 2020. Vol. 245. No. 3. P. 341 – 349.

16. Abdushukurov A., Nurmukhamedova N. Asymptotic properties of likelihood ratio statistics in competing risks model under interval random censoring / Lobachevskii J. Math. 2021. Vol. 42. No. 12. P. 2687 – 2696.

17. Kurasov O. A., Burkov P. V. Competing risks analysis of engineering system failure based on nonparametric prediction / Vestn. Tomsk. Gos. Arkhitekt.-Stroit. Univ. 2024. Vol. 26. No. 2. P. 93 – 103 [in Russian]. DOI: 10.31675/1607-1859-2024-26-2-93-103

18. Abdushukurov A., Nurmukhamedova N., Erisbaev S. Fisher information contained in incomplete observations / Industr. Lab. Mater. Diagn. 2024. Vol. 90. No. 7. P. 84 – 92 [in Russian]. DOI: 10.26896/1028-6861-2024-90-7-84-92

19. Shiryaev A. N. Probability. — Moscow: Nauka, 1989. — 638 p. [in Russian].


Review

For citations:


Nurmukhamedova N.S. Fisher information in a competing risks model with inhomogeneous random interval censoring. Industrial laboratory. Diagnostics of materials. 2025;91(7):85-93. (In Russ.) https://doi.org/10.26896/1028-6861-2025-91-7-85-93

Views: 21


ISSN 1028-6861 (Print)
ISSN 2588-0187 (Online)