| Nowadays Weibull family and its extensions are widely used for analyzing life time data, one of which is generalized power Weibull (GPW) distribution. The GPW distributions not only allow for a broad class of monotone hazard rates but also contain distributions with unimodal or bathtub shaped hazard rates. Additionally, the variables in reality often have some correlation or dependence. Sometimes the correlations are linear or approximately linear, but sometimes the correlations are nonlinear. So a location-scale nonlinear regression model based on the GPW distribution is proposed.In survival analysis, it often occurs that observed data is censored. Interval-censored data widely involved in engineering, biology and medical science is one important and significant type of censored data. In practice, the event of experimental object is not observed exactly for various reasons but is only known to occur within some time interval. Such data is so called interval-censored data. For getting the information of research object, it is necessary to do some study under the interval-censored samples.The quality of parameter estimation which is the most important problem in model study directly affects the accuracy of statistical results. Further more, statistical diagnosis which examines the aspects or outlooks of statistical inference is an important component of statistical analysis. Statistical analysis for log-GPW nonlinear regression model with interval-censored data is systematically studied. Firstly, the maximum likelihood estimates for model parameters are obtained. Then not only the one-step approximations of the MLEs are given, but also the generalized Cook's distance, W-K measures and likelihood distance as well as their one-step approximations are given based on global influence diagnostics. Using local influence diagnostics, the normal curvatures of local influence are derived under case-weight perturbation and explanatory variable perturbation. Further more, some examples based on Monte Carlo simulation are given to illustrate the effectiveness of parametric estimation as well as diagnostic statistics obtained in this paper. Finally, the assumptions in the model are checked by residual analysis, such as adjusted Cox-Snell residuals, martingale residuals and modified deviance residuals. |
