In this thesis, a general approach for correcting the bias of an estimator and for obtaining estimates of the accuracy of the bias-corrected estimator is proposed. The method, entitled extended bootstrap bias correction (EBS), is based on the bootstrap resampling technique and attempts to identify the functional relationship between the estimates obtained from the original and bootstrap samples and the true parameter values, drawn from a plausible parameter space. The bootstrap samples are used for studying the behaviour of the bias and, consequently, for the bias correction itself. The EBS approach is assessed by extensive Monte Carlo studies in three different applications of multilevel analysis of survey data. First, the proposed EBS method is applied to bias adjustment of unweighted and probability weighted estimators of two-level model parameters under informative sampling designs with small sample sizes. Second, the EBS approach is considered for estimating the mean squared error (MSE) of predictors of small area means under the area level Fay-Herriot model for different distributions of the model error terms. Finally, the EBS procedure is applied to MSE estimation of predictors of small area proportions under a unit level generalized linear mixed model. The general conclusion emerging from this thesis is that the EBS approach is effective in providing bias corrected estimators in all the three cases considered.