#### Degree Type

Dissertation

#### Date of Award

1987

#### Degree Name

Doctor of Philosophy

#### Department

Statistics

#### Abstract

A hazard function which initially decreases, then drops down to an essentially constant level, and then increases due to aging, often is described as being "U-shaped" or "bathtub-shaped." For such a hazard function h(·), the model interval M is defined as M = m |h(m) = inf h(x), which is an interval over which the hazard rate is constant;Bray et al. (1967) developed the maximum likelihood estimate cx h(·) of a U-shaped hazard function h(·), with cx h(·) certain to equal zero over some open interval, and showed that, if h(·) is "V-shaped," then cx h(·) is strongly consistent at all continuity points of h(·), excepting the "turning point" (i.e., minimizing point, of a "V-shaped" h(·));Let [alpha](n) be such that both [alpha](n) and n/[alpha](n) tend to infinity with n. This dissertation presents a maximum likelihood estimate h(·) of h(·) that is restricted to attain its minimum value at least [alpha](n) consecutive observations. This estimator h(·) everywhere exceeds zero, and is strongly consistent at the continuity points of h(·). While Bray et al. (1967) make use of the well-known "Pooled-Adjacent-Violators" algorithm named by Barlow et al. (1972) for monotone estimation, which involves successive revisions at neighboring observation pairs, the algorithmic computation of h(·) proceeds by successive revisions at neighboring observation triplicates.

#### DOI

https://doi.org/10.31274/rtd-180813-10635

#### Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

#### Copyright Owner

Mong-Hong Lee

#### Copyright Date

1987

#### Language

en

#### Proquest ID

AAI8721903

#### File Format

application/pdf

#### File Size

81 pages

#### Recommended Citation

Lee, Mong-Hong, "Strongly consistent modified maximum likelihood estimation of U-shaped hazard functions " (1987). *Retrospective Theses and Dissertations*. 11701.

https://lib.dr.iastate.edu/rtd/11701