In this paper, the novel estimating methods and their properties for pth-order dependence-driven random coefficient integer-valued autoregressive time series model (DDRCINAR(p)) are studied as the innovation sequence has a Poisson distribution and the thinning is binomial. Strict stationarity and ergodicity for DDRCINAR(p) model are proved. Conditional maximum likelihood and conditional least squares are used to estimate the model parameters. Asymptotic normality of the proposed estimators are derived. Finite sample properties of the conditional maximum likelihood estimator are examined in relation to the widely used conditional least squares estimator. It is concluded that, if the Poisson assumption can be justified, conditional maximum likelihood method performs better in terms of bias and MSE. Finally, three real data sets are analyzed to demonstrate the practical relevance of the model.

This paper considers the nonparametric estimation of a failure time distribution function when only doubly censored data are available, which occurs in many situations such as epidemiological studies. In these situations, the failure time of interest is defined as the elapsed time between an initial event and a subsequent event, and the observations on both events can suffer censoring. As a consequence, the estimation is much more complicated than that for right- or interval-censored failure time data both theoretically and practically. For the problem, although several procedures have been proposed, they are only ad hoc approaches as the asymptotic properties of the resulting estimates are basically unknown. We investigate both the consistency and the convergence rate of a commonly used nonparametric estimate and show that as expected, the estimate is slower than that with right-censored or interval-censored data. Furthermore, we establish the asymptotic normality of the smooth functionals of the estimate and present a nonparametric test procedure for treatment comparison.