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...

Se estudia la estimación de tipo no paramétrico de la función de riesgo o razón de fallo de una variable aleatoria real. A partir de una muestra X1, X2, ..., Xn de datos no censurados y no necesariamente independientes, se considera un estimador cociente entre el estimador núcleo de la función de densidad y un estimador núcleo de la función de supervivencia, sobre el que se estudia el problema de selección del parámetro ventana. Por medio de un estudio de simulación se observa la ventaja de utilizar...

The shape parameter of the Topp-Leone distribution is estimated from classical and Bayesian points of view based on Type I censored samples. The maximum likelihood and the approximate maximum likelihood estimates are derived. The Bayes estimate and the associated credible interval are approximated by using Lindley's approximation and Markov Chain Monte Carlo using the importance sampling technique. Monte Carlo simulations are performed to compare the performances of the proposed methods. Real and...

An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.

An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.

We consider a failure hazard function, conditional on a time-independent covariate Z, given by ${\eta }_{{\gamma }^0}\left(t\right)f_{{\beta }^0}\left(Z\right)$. The baseline hazard function ${\eta }_{{\gamma }^0}$ and the relative risk $f_{{\beta }^0}$ both belong to parametric families with ${\theta }^0={({\beta }^0,{\gamma }^0)}^{\top }\in {ℝ}^{m+p}$. The covariate Z has an unknown density and is measured with an error through an additive error model U = Z + ε where ε is a random variable, independent from Z, with known density $f_{\epsilon }$. We observe a n-sample (Xi, Di, Ui), i = 1, ..., n, where Xi is the minimum between the failure time and the censoring time, and...

In the article, we propose a new estimator of the hazard rate function in the framework of the multiplicative point process intensity model. The technique combines the reflection method and the method of transformation. The new method eliminates the boundary effect for suitably selected transformations reducing the bias at the boundary and keeping the asymptotics of the variance. The transformation depends on a pre-estimate of the logarithmic derivative of the hazard function at the boundary.

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.

Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in $L_1$ are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data example is...