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...

In this paper we describe the so-called indirect method of inference, originally developed from the econometric literature, and apply it to survival analyses of two data sets with repeated events. This method is often more convenient computationally than maximum likelihood estimation when handling such model complexities as random effects and measurement error, for example; and it can also serve as a basis for robust inference with less stringent assumptions on the data generating mechanism. The...

In this paper we consider three measures of overlap, namely Matusia’s measure $\rho$, Morisita’s measure $\lambda$ and Weitzman’s measure $\Delta$. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...

In this paper we consider three measures of overlap, namely Matusia's measure ρ, Morisita's measure λ and Weitzman's measure Δ. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...

We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation al the likelihood for the illness-death model based on applying Jacod´s formula to an observed bivariate counting...

This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.

Several aspects of the analysis of two successive survival times are considered. All the analyses take into account the dependent censoring on the second time induced by the first. Three nonparametric methods are described, implemented and applied to the data coming from a multicentre clinical trial for HIV-infected patients. Visser's and Wang and Wells methods propose an estimator for the bivariate survival function while Gómez and Serrat's method presents a conditional approach for the second...

In the framework of a stochastic optimization problem, it is assumed that the stochastic characteristics of optimized system are estimated from randomly right-censored data. Such a case is frequently encountered in time-to-event or lifetime studies. The analysis of precision of such a solution is based on corresponding theoretical properties of estimated stochastic characteristics. The main concern is to show consistency of optimal solution even in the random censoring case. Behavior of solutions...

Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore,...