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The main focus of many agricultural, ecological and environmental studies is to develop well designed, cost-effective and efficient sampling designs. Ranked set sampling (RSS) is one of those sampling methods that can help accomplish such objectives by incorporating prior information and expert knowledge to the design. In this thesis, new RSS schemes are suggested for efficiently estimating the population mean. These sampling schemes can be used as cost-effective alternatives to the traditional simple random sampling (SRS) and RSS schemes. It is shown that the mean estimators under the proposed sampling schemes are at least as efficient as the mean estimator with SRS. We consider the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) for the unknown parameters (location and scale) of a location-scale family of distributions under double RSS (DRSS) scheme. The BLUEs and BLIEs with DRSS are more precise than their counterparts based on SRS and RSS schemes. We also consider the BLUEs based on DRSS and ordered DRSS (ODRSS) schemes for the unknown parameters of a simple linear regression model using replicated observations. It turns out that, in terms of relative efficiencies, the BLUEs under ODRSS are better than the BLUEs with SRS, RSS, ordered RSS (ORSS) and DRSS schemes. Quality control charts are widely recognized for their potential to be a powerful process monitoring tool of the statistical process control. These control charts are frequently used in many industrial and service organizations to monitor in-control and out-of-control performances of a production or manufacturing process. The RSS schemes have had considerable attention in the construction of quality control charts. We propose new exponentially weighted moving average (EWMA) control charts for monitoring the process mean and the process dispersion based on the BLUEs obtained under ORSS and ODRSS schemes. We also suggest an improved maximum EWMA control chart for simultaneously monitoring the process mean and dispersion based on the BLUEs with ORSS scheme. The proposed EWMA control charts perform substantially better than their counterparts based on SRS and RSS schemes. Finally, some new EWMA charts are also suggested for monitoring the process dispersion using the best linear unbiased absolute estimators of the scale parameter under SRS and RSS schemes.

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This thesis deals with the bootstrap method. Three decades after the seminal paper by Bradly Efron, still the horizons of this method need more exploration. The research presented herein has stepped into different fields of statistics where the bootstrap method can be utilized as a fundamental statistical tool in almost any application. The thesis considers various statistical problems, which is explained briefly below. Bootstrap method: A comparison of the parametric and the nonparametric bootstrap of variance is presented. The bootstrap of ranked set sampling is dealt with, as well as the wealth of theories and applications on the RSS bootstrap that exist nowadays. Moreover, the performance of RSS in resampling is explored. Furthermore, the application of the bootstrap method in the inference of contingency table test is studied. Coefficient of variation: This part shows the capacity of the bootstrap for inferring the coefficient of variation, a task which the asymptotic method does not perform very well. Information theory: There are few works on the study of information theory, especially on the inference of entropy. The papers included in this thesis try to achieve the inference of entropy using the bootstrap method.