Consider the model "Y"&equals;"&bgr;"-super-′<b>X</b>&plus;"&epsi;". Let "F"₀ be the unknown cumulative distribution function of the random variable "&epsi;". Consistency of the semi-parametric Maximum likelihood estimator of ("&bgr;","F"₀), denoted by <formula format="inline"><file name="sjos_491_mu1.gif" type="gif" /></formula>, has not been established under any interval censorship (IC) model. We prove...

Consider nonparametric problems of estimating an unknown distribution function, F, under the loss L(F,a)=[integral operator] F(t)-a(t)2(F(t))[alpha](1 -F(t))[beta]dF(t), where [alpha][set membership, variant][-1,0] and [beta][set membership, variant][-1,1]. It is proved that the Empirical...

Cox's proportional hazards (PH) model is applicable to continuous random (response) variables as well as to discontinuous ones. We make two remarks on the PH models for discontinuous random (response) variables. (1) In general, the proportional hazards relation can only occur in the interior of...

In case 2 interval censoring the random survival time X of interest is not directly observable, but only known to have occurred before Y, between Y and Z, or after Z, where (Y, Z) is a pair of observable inspection times such that Y Z. We consider the large sample properties of the generalized...