This article considers the inference for a competing risks model with a partially observed failure cause when latent failure times follow Burr XII distributions. Inference is obtained under a generalized progressive hybrid censoring. Estimations of unknown parameters under different restrictions are provided using frequentist and Bayesian approaches. Subsequently, interval estimators are also derived. Bayesian estimators are developed for order-restricted parameters and are compared with corresponding likelihood estimators. The case of unrestricted parameters is considered as well. The performance of all estimators is evaluated based on a simulation study, and a real data set is also presented for illustrative purposes.