21 research outputs found
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Bandwidth selection in marker dependent kernel hazard estimation
Practical estimation procedures for the local linear estimation of an unrestricted failure rate when more information is available than just time are developed. This extra information could be a covariate and this covariate could be a time series. Time dependent covariates are sometimes called markers, and failure rates are sometimes called hazards, intensities or mortalities. It is shown through simulations and a practical example that the fully local linear estimation procedure exhibits an excellent practical performance. Two different bandwidth selection procedures are developed. One is an adaptation of classical cross-validation, and the other one is indirect cross-validation. The simulation study concludes that classical cross-validation works well on continuous data while indirect cross-validation performs only marginally better. However, cross-validation breaks down in the practical data application to old-age mortality. Indirect cross-validation is thus shown to be superior when selecting a fully feasible estimation method for marker dependent hazard estimation
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Smoothing survival densities in practice
Many nonparametric smoothing procedures consider independent identically distributed stochastic variables. There are also many important nonparametric smoothing applications where the data is more complicated. Survival data or filtered data, defined as following Aalen’s multiplicative hazard model and aggregated versions of this model, are considered. Aalen’s model based on counting process theory allows multiple left truncations and multiple right censoring to be present in the data. This type of filtering is omnipresent in biostatistical and demographical applications, where people can join a study, leave the study and perhaps join the study again. The estimation methodology is based on a recent class of local linear density estimators. A new stable bandwidth-selector is developed for these estimators. A data application to aggregated national mortality data is provided, where immigrations to and from the country correspond to respectively left truncation and right censoring. The aggregated mortality data study illustrates that the new practical density estimators provide an important extra element in the visual toolbox for understanding survival data
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Double one-sided cross-validation of local linear hazards
This paper brings together the theory and practice of local linear kernel hazard estimation. Bandwidth selection is fully analysed, including Do-validation that is shown to have good practical and theoretical properties. Insight is provided into the choice of the weighting function in the local linear minimization and it is pointed out that classical weighting sometimes lacks stability. A new semiparametric hazard estimator transforming the survival data before smoothing is introduced and shown to have good practical properties
Bias reduction in nonparametric hazard rate estimation
The need of improvement of the bias rate of convergence of traditional nonparametric hazard rate estimators has been widely discussed in the literature. Initiated by recent developments in kernel density estimation we distinguish and extend three popular bias reduction methods to the hazard rate case. A usual problem of fixed kernel hazard rate estimates is their poor performance at endpoints. Noticing the automatic boundary adaptive property of the local linear smoother (Fan and Gijbels [13]) we adapt the method to the hazard rate case and we show that it results in estimators with bias at endpoints reduced to the level of interior bias. We then turn our attention to global bias problems. Utilizing the proposals of Hall and Marron [16] for estimation using location varying bandwidth as a means to improve the bias rate of convergence, we extend two distinct hazard rate estimators to the point that they make use of the method. The theoretical study of the resulting estimators verifies this improvement. A somewhat related way of improvement over the ordinary kernel estimates of the hazard rate is attained by extending the method of empirical transformations (Ruppert and Cline [35]). Studying the asymptotic square error of the resulting estimator we show that the advance is similar to the variable bandwidth approach. In summarizing the thesis, ideas and plans for further work are suggested