Smoothing Hazard Functions and Time-Varying Effects in Discrete Duration and Competing Risks Models
提出一种基于后验众数估计的平滑方法，通过惩罚似然和卡尔曼滤波高效估计离散持续时间数据中的风险函数和时变效应，并应用于德国社会经济面板数据。
Abstract State-space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger datasets. Therefore, based on previous work on filtering and smoothing for multicategorical time series and longitudinal data, our approach uses posterior mode estimation. Thus we have to maximize posterior densities or, equivalently, a penalized likelihood, which enforces smoothness of hazard functions and time-varying effects by a roughness penalty. Dropping the Bayesian smoothness prior and adopting a nonparametric viewpoint, one might also start directly from maximizing this penalized likelihood. We show how Fisher scoring smoothing iterations can be carried out efficiently by iteratively applying linear Kalman filtering and smoothing to a working model. This algorithm can be combined with an EM-type procedure to estimate unknown smoothing parameters or hyperparameters. The methods are applied to a larger set of unemployment duration data with one terminating event and, in a further analysis, multiple terminating events from the German socioeconomic panel GSOEP.