Multivariate Threshold Regression Models with Cure Rates: Identification and Estimation in the Presence of the Esscher Property

The first hitting time of a boundary or threshold by the sample path stochastic process is central concept regression models for survival data analysis. Regression functions and parameters in these are multivariate combinations explanatory variates. under investigation may be univariate process. processes interest to us this report those that possess stationary independent increments (i.e., Lévy processes) as well Esscher property. transform transformation probability density has applications actuarial science, financial engineering, other fields. with property often encountered practical applications. Frequently, also involve ‘cure rate’ fraction because some individuals susceptible failure others not. Cure rates arise endogenously from model alone exogenously mixing distinct statistical populations set. We show, using both theoretical analysis case demonstrations, estimates derived typical not able distinguish between cure rate who but escape fate chance. ambiguity aggravated right censoring times minor misspecifications model. Slightly incorrect specifications can lead problems identification estimation. In situation, additional guidance estimating non-susceptibles must come subject matter expertise types than times, censored otherwise. identifiability issue confronted directly present when applying kinds commonly used Other methods, however, usually do provide framework recognizing dealing so unintentionally ignored. foundations work set out, which presents new somewhat surprising results distributions have