In practice, it often occurs that some covariates of interest are not measured because of various reasons, but there may exist some auxiliary information available. In this case, an issue of interest is how to make use of the available auxiliary information for statistical analysis. This paper discusses statistical inference problems in the context of current status data arising from an additive hazards model with auxiliary covariates. An empirical log-likelihood ratio statistic for the regression...

The Nelson-Aalen estimator is widely used in biostatistics as a non-parametric estimator of the cumulative hazard function based on a right censored sample. A number of alternative estimators can be mentioned, namely, the naive local constant estimator (Guillén, Nielsen and Pérez-Marín, 2007) which provides improved bias versus variance properties compared to the traditional Nelson-Aalen estimator. Nevertheless, an empirical comparison of these two estimators has never been carried out. In this...

A partir de una muestra de datos de supervivencia que contiene valores no observados en las covariantes de interés, presentamos una metodología que permite extraer toda la información contenida en covariantes completamente observadas, que estén fuertemente correlacionadas con las citadas covariantes de interés. El enfoque utilizado es completamente paramétrico y se basa en el método de máxima verosimilitud. Mostramos las dificultades, tanto de índole práctica como filosófica, que aparecen en la...

The subject of this paper is to estimate adaptively the common probability density of $n$ independent, identically distributed random variables. The estimation is done at a fixed point $x_0\in ℝ$, over the density functions that belong to the Sobolev class $W_n(\beta ,L)$. We consider the adaptive problem setup, where the regularity parameter $\beta$ is unknown and varies in a given set $B_n$. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point $x_0\in ℝ$, over the density functions that belong to the Sobolev class Wn(β,L). We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.