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Abstract
This thesis is concerned with the problem of estimating and assessment of the sampling relative error for the population total parameter in one of the complex sampling designs, by what we mean stratified random sampling design, this contrary to the well-known simple random sampling design. The estimation is frequently a problem and very useful as it is a measure of precision. In the middle of the last century an attention has been directed to a new inferential methodology to solve this problem, known as resampling, to which the most important resampling methods, such as the jackknife and the bootstrap, belong. So, this thesis addresses the problem of estimating the sampling relative error in resampling techniques, introduces the generalizations of chao et al. (2013) jackknife estimators, and studies the performance of the mentioned estimators in comparison with the traditional method which known as the plug-in method. A monte Carlo simulation study is conducted to assess the performance of the estimators under two different distributions, normal and exponential, for different allocations of the stratified sampling design; equal, proportional, optimum, and Neyman allocation and for simple random sampling design. Based on the simulation results it is shown that under normal distribution the location estimators are more accurate than the other methods. But, under exponential distribution the proposed jackknife leaving group of strata out is more accurate than the other methods and the bootstrap method may be match