The nonparametric approach to estimate hazard rates for lifetime data is flexible, model-free and data-driven. No shape assumption is imposed other than that the hazard function is a smooth function. Such an approach typically involves smoothing of an initial hazard estimate, with arbitrary choice of smoother. We describe methods for grouped lifetime data observed at certain time intervals and ...

Abstract: Structures such as independence of random variables in probability densities and hazard proportionality in covariate dependent hazard functions have important interpretations in statistical analysis. Such structures can be characterized by term eliminations from an analysis of variance (ANOVA) decomposition in log density or log hazard. Nonparametric estimation of these functions with...

The field of hazard function analysis (HFA) involves a probabilistic assessment of the ‘‘time to failure’’ or ‘‘return period,’’ T, of an event of interest. HFA is used in epidemiology, manufacturing, medicine, actuarial statistics, reliability engineering, economics, and elsewhere. For a stationary process, the probability distribution function (pdf) of the return period always follows an expo...

In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of...

The soundness and efficiency of banks is one of the important subjects that neglecting it can have adverse consequences for every country's economy. For economies depending on the money market, such as the Iran economy, this subject is more critical. Therefore, in this study, using panel data related to 16 Iranian banks for the annual period of 2010-2017, the economic efficiency was determined ...

In the analysis of competing risk data, the observed effect of a covariate can be obtained via a Fine and Gray sub-distribution hazard ratio. Sometimes, it is also desirable to obtain the virtual effect of a covariate as if the competing risks were non-existent. Under the latent failure time scenario, when the event of interest and the competing risk event are independent, the cause-specific ha...

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...