On the Application of the Bootstrap : Coefficient of Variation, Contingency Table, Information Theory and Ranked Set Sampling

Abstract: 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.