Kernel estimation of hazard functions when observations have dependent and common covariates

Abstract

We propose a hazard model where dependence between events is achieved by assuming dependence between covariates. This model allows for correlated variables speci…c to observations as well as macro variables which all observations share. This setup better …ts many economic and …nancial applications where events are not independent. Nonparametric estimation of the hazard function is then studied. Kernel estimators proposed in Nielsen and Linton (1995, Annals of Statistics) and Linton, Nielsen and Van de Geer (2003, Annals of Statistics) are shown to have similar asymptotic properties compared with the i:i:d: case.Mixing conditions ensure the asymptotic results follow. These results depend on adjustments to bandwidth conditions. Simulations are conducted which verify the impact of dependence on estimators. Bandwidth selection accounting for dependence is shown to improve performance. In an empirical application, trade intensity in high-frequency …nancial data is estimated.

A General Semiparametric Approach to Inference with Marker-Dependent Hazard Rate Models

“…As an obvious topic for further research one may consider the inclusion of unobserved heterogeneity or frailty terms in the individual hazard rates. Indeed, recent advances in the econometric literature about duration models have emphasized the need for a flexible estimation structure in the context of mixed proportional hazard estimation, see for example Bijwaard et al (2013), Wolter (2016) and Hausman and Woutersen (2014). While these papers make important contributions in the way that they relax certain parametric assumptions, they share the inflexibility of the parametric form of the covariate function, so there lies potential for further research.…”

“…It requires the assumption that the covariates W (t) affect the hazard rate by way of the parametric functional form exp{β ′ W (t)} and it does not include unobserved heterogeneity. The recent econometric literature has focused on the latter problem with major contributions from for example Bijwaard et al (2013) and Wolter (2016), who provide extensions to the Cox model to accommodate unobserved heterogeneity, and Hausman and Woutersen (2014) who propose a semiparametric estimator for discrete duration data. In contrast, in this paper we focus on relaxing the assumptions associated with the covariate function and we concentrate on continuous data.…”

Comparison of parametric and semiparametric survival regression models with kernel estimation

“…C i ∼ log N (2.5, 0.2 2 ) independent of the covariates and survival times. An uniform distribution of censoring times on the interval (5,20) was used, but it is not referred to in this paper. See [41] for details how given censoring time distribution parameters with predefined censoring rates were determined.…”

“…Extending kernel estimators by assuming dependence between covariates was proposed by Linton et al [19] with restriction to additive or multiplicative hazard functions. These results were extended by Wolter [20], who introduced a simulation study examining the effect of dependence on finite sample properties of the relevant estimators.…”