×

zbMATH — the first resource for mathematics

Monotonic estimators for the survival function of quality adjusted lifetime. (English) Zbl 1073.62086
Summary: The simple weighted estimator of the survival function of quality adjusted lifetime is a consistent estimator and a proper survival function. It is considerably less efficient than many estimators that are not monotonic and therefore are not proper survival functions. The non-monotonic estimators can be modified to be monotonic, but additional work is required to determine the effect of the modification on their consistency and efficiency. As a prelude to the main results, we introduce a new non-monotonic estimator and study the positive and negative mass jump points of three estimators. This article proposes several classes of monotonic estimators for the survival function of quality adjusted life. All proposed estimators are shown to be consistent. Two proposed estimators are nearly as efficient as their non monotonic counterparts, when the sample size is large.

MSC:
62N02 Estimation in survival analysis and censored data
62F12 Asymptotic properties of parametric estimators
62N01 Censored data models
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Almanassra , M. (2003). Estimation of survival and cumulative-hazard functions of restricted quality adjusted lifetime. Ph.D. Dissertation, Department of Mathematics, Southern Illinois University Carbondale .
[2] DOI: 10.2307/2982889 · Zbl 04509731 · doi:10.2307/2982889
[3] DOI: 10.1214/aos/1176351049 · Zbl 0653.62071 · doi:10.1214/aos/1176351049
[4] DOI: 10.2307/2684631 · Zbl 04527594 · doi:10.2307/2684631
[5] Huang Y., J. Amer. Statist. Assoc. 53 pp 457– (1998)
[6] DOI: 10.2307/2281868 · Zbl 0089.14801 · doi:10.2307/2281868
[7] DOI: 10.1093/biomet/80.3.535 · Zbl 0800.62704 · doi:10.1093/biomet/80.3.535
[8] Oakes D., Biometrika 1 pp 99– (2000) · Zbl 1073.62560
[9] DOI: 10.1093/biomet/79.3.495 · Zbl 0764.62095 · doi:10.1093/biomet/79.3.495
[10] DOI: 10.1214/aos/1176347992 · Zbl 0738.62049 · doi:10.1214/aos/1176347992
[11] DOI: 10.2307/2669760 · Zbl 1008.62098 · doi:10.2307/2669760
[12] Wang , J. Estimation of quality adjusted survival functions and mean lifetime medical cost. Ph.D. Dissertation, Department of Mathematics, Southern Illinois University at Carbondale .
[13] DOI: 10.1093/biomet/84.2.339 · Zbl 0882.62110 · doi:10.1093/biomet/84.2.339
[14] DOI: 10.1111/j.0006-341X.1999.01101.x · Zbl 1059.62742 · doi:10.1111/j.0006-341X.1999.01101.x
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.