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Empirical analysis of current status data for additive hazards model with auxiliary covariates

Jianling Zhang, Mei Yang, Xiuqing Zhou (2021)

Kybernetika

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...

Empirical comparison between the Nelson-Aalen Estimator and the Naive Local Constant Estimator.

Ana María Pérez-Marín (2008)

SORT

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...

Estimación bayesiana de una función de fiabilidad con conocimiento a priori gamma expendido.

Domingo Morales, Leandro Pardo, Vicente Quesada (1987)

Trabajos de Investigación Operativa

Se plantea el problema de estimar una función de fiabilidad en el contexto bayesiano no paramétrico, pero utilizando técnicas paramétricas de estimación en procesos estocásticos. Se define el proceso gamma extendido, cuyas trayectorias son tasas de azar crecientes cuando se eligen convenientemente los parámetros del proceso. Se obtienen estimadores basados en este proceso, se estudian sus propiedades asintóticas bayesianas, y se termina con un ejemplo de aplicación mediante simulación.

Estimación no paramétrica de la función de riesgo: aplicaciones a sismología.

Graciela Estévez Pérez, Alejandro Quintela del Río (2001)

Qüestiió

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...

Estimación paramétrica bayesiana no paramétrica de funciones de supervivencia con observaciones parcialmente censuradas.

Domingo Morales, Vicente Quesada, Leandro Pardo (1986)

Trabajos de Estadística

The problem of nonparametric estimation of a survival function based on a partially censored on the right sample is established in a Bayesian context, using parametric Bayesian techniques. Estimates are obtained considering neutral to the right processes, they are particularized to some of them, and their asymptotic properties are studied from a Bayesian point of view. Finally, an application to a Dirichlet process is simulated.

Estimates of reliability for the normal distribution

Jan Hurt (1980)

Aplikace matematiky

The minimum variance unbiased, the maximum likelihood, the Bayes, and the naive estimates of the reliability function of a normal distribution are studied. Their asymptotic normality is proved and asymptotic expansions for both the expectation and the mean squared error are derived. The estimates are then compared using the concept of deficiency. In the end an extensive Monte Carlo study of the estimates in small samples is given.

Estimating the shape parameter of the Topp-Leone distribution based on Type I censored samples

Husam Awni Bayoud (2015)

Applicationes Mathematicae

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...

Estimation of parameters in a network reliability model with spatial dependence

Ian Hepburn Dinwoodie (2010)

ESAIM: Probability and Statistics

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.

Estimation of parameters in a network reliability model with spatial dependence

Ian Hepburn Dinwoodie (2005)

ESAIM: Probability and Statistics

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.

Estimation of the hazard function in a semiparametric model with covariate measurement error

Marie-Laure Martin-Magniette, Marie-Luce Taupin (2009)

ESAIM: Probability and Statistics

We consider a failure hazard function, conditional on a time-independent covariate Z, given by η γ 0 ( t ) f β 0 ( Z ) . The baseline hazard function η γ 0 and the relative risk f β 0 both belong to parametric families with θ 0 = ( β 0 , γ 0 ) ⊤ ∈ 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 ε . 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...

Estimation of the hazard rate function with a reduction of bias and variance at the boundary

Bożena Janiszewska, Roman Różański (2005)

Discussiones Mathematicae Probability and Statistics

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.

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