## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 7, Number 3 (2013), 1474-1496.

### Estimating restricted mean job tenures in semi-competing risk data compensating victims of discrimination

Qing Pan and Joseph L. Gastwirth

#### Abstract

When plaintiffs prevail in a discrimination case, a major component of the calculation of economic loss is the length of time they would have been in the higher position had they been treated fairly during the period in which the employer practiced discrimination. This problem is complicated by the fact that one’s eligibility for promotion is subject to termination by retirement and both the promotion and retirement processes may be affected by discriminatory practices. This semi-competing risk setup is decomposed into a retirement process and a promotion process among the employees. Predictions for the purpose of compensation are made by utilizing the expected promotion and retirement probabilities of similarly qualified members of the nondiscriminated group. The restricted mean durations of three periods are estimated—the time an employee would be at the lower position, at the higher level and in retirement. The asymptotic properties of the estimators are presented and examined through simulation studies. The proposed restricted mean job duration estimators are shown to be robust in the presence of an independent frailty term. Data from the reverse discrimination case, *Alexander v. Milwaukee*, where White-male lieutenants were discriminated in promotion to captain are reanalyzed. While the appellate court upheld liability, it reversed the original damage calculations, which heavily depended on the time a plaintiff would have been in each position. The results obtained by the proposed method are compared to those made at the first trial. Substantial differences in both directions are observed.

#### Article information

**Source**

Ann. Appl. Stat., Volume 7, Number 3 (2013), 1474-1496.

**Dates**

First available in Project Euclid: 3 October 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1380804803

**Digital Object Identifier**

doi:10.1214/13-AOAS637

**Mathematical Reviews number (MathSciNet)**

MR3127955

**Zentralblatt MATH identifier**

1283.62237

**Keywords**

Compensation equal employment job tenures lost chance doctrine restricted mean lifetime semi-competing risks

#### Citation

Pan, Qing; Gastwirth, Joseph L. Estimating restricted mean job tenures in semi-competing risk data compensating victims of discrimination. Ann. Appl. Stat. 7 (2013), no. 3, 1474--1496. doi:10.1214/13-AOAS637. https://projecteuclid.org/euclid.aoas/1380804803