Summary: This study considers the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian frameworks when samples are observed in the presence of progressively type-I hybrid censoring. Under classical approach, we employ EM and stochastic EM algorithm for obtaining the maximum likelihood estimators of model parameters. On the other hand, under Bayesian framework, we obtain Bayes estimators with respect to different symmetric and asymmetric loss functions under non-informative and informative priors. In this regard, we use Tierney-Kadane and importance sampling methods. Asymptotic normality theory and MCMC samples are employed to construct the confidence intervals and HPD credible intervals. To improve the estimation accuracy shrinkage pre-test estimation strategy is also suggested. The relative efficiency of these estimators with respect to both classical and Bayesian estimators are investigated numerically. Our simulation studies reveal that the shrinkage pre-test estimation strategy outperforms the estimation based on classical and Bayesian procedure. Finally, one real data set is analyzed to illustrate the methods of inference discussed here.