Estimation of piecewise constant mixed proportional hazard competing risk model with NPMLE. The model is described in S. Gaure et al. (2007) <doi:10.1016/j.jeconom.2007.01.015>, J. Heckman and B. Singer (1984) <doi:10.2307/1911491>, and B.G. Lindsay (1983) <doi:10.1214/aos/1176346059>.