Speaker :Dr. Suchismita Das

Abstract :
A Class of Semiparametric Regression Models Suchismita Das Abstract In the analysis of lifetimes, multiple regression is a conventional technique for investigating the relationship between the lifetimes, dependent variables and possible prognostic variables x1, x2, . . ., xn. The Cox’s (1972) proportional hazards model used to establish the dependency of the lifetime of a subject X∗ with the baseline random variable X, through the covariates x = (x1, x2, . . ., xn), where the covariates are taken to be constant. In some practical situations, the covariates may not be constant over the whole time interval [0, ∞), but they may vary over different time intervals ti−1 6 t < ti , for i = 1, 2, . . . , with t0 ≡ 0. This type of models may be called piecewise proportional model. In a more general case, when the intervals [ti−1, ti) become smaller and smaller, we get a model where the covariates are time dependent. It is worth mentioning here that the time dependent covariates could also be used in a regression model with time varying slopes. It is well known that regression model is used in different situations, especially when forecasting is required. In reliability analysis, the reliability of any product or system depends on number of factors which again, may vary with time. In order to take care of these kind of problems, we introduce the dynamic proportion models. These semiparametric models are used for estimating the risk of failure associated with a vector of covariates. But, in the literature, there are almost no discussion on the effects of unexplained heterogeneity for alternative semiparametric regression models. This motivates us to study a class of semiparimetric linear transformation model with time dependent covariates, which includes the dynamic proportional models as special cases. We call this model as dynamic linear transformation (DLT) model.