A Wavelet Estimator of the Intensity Function with Censored Data

An estimator of baseline intensity by the method of wavelets

“…The proof of this lemma can be found in [8] Proof of Theorem 3.1 i) Using the pseudo-estimator (11), we have…”

“…Lemma 3.2 Given the estimator defined in (8) and the pseudo-estimator defined in (11). The following result holds almost surely:…”

“…In a non-parametric estimation of intensity function, several papers have been published using a wide range of techniques such as kernels [1], [2] and [3], penalized likelihood [4] and wavelet approach [5], [6], [7] and [8]. Intensity estimation applies in the area of survival analysis, reliability and medical experiments.…”

A strong linear representation for the maximum conditional hazard rate estimator in survival analysis

“…Afterward, authors among [36,31,40,7], worked in this field. In the context of censored response data considered in a regression model with fully observable covariates, much researches has been devoted to the nonparametric estimation of the conditional hazard function.…”

On the strong convergence of the hazard rate and its maximum risk point estimators in presence of censorship and functional explanatory covariate

“…Nonparametric methods based on convolution by kernels ideas, which are known for their good behavior in problems of probability density estimation (conditional or not), are also widely used in the nonparametric estimation of the hazard function. Mention may in particular be made of the recent articles by Gneyou (1997), Gefeller and Michels (1992) Laksaci and Mechab (2010), Dupuy and Gneyou (2011), as examples and references therein. A wide range of literature in this field is provided by Tanner and Wong (1983), Singpurwalla and Wong (1983), Hassani and al.…”