Some Laws Of Large Numbers For The Dependent Bootstrap Mean

This dissertation consists of three chapters, which is completed during my MasterDegree of Science. We try to derive some laws of large numbers for the dependent boot-strap sample mean.In chapter one, we introduce the concept of the dependent bootstrap proposed bySmith and Taylor, and other definitions and properties related to our results.In 2005, Einmahl and Rosalsky established very general weak laws of large numbersfor Efron's nonparametric bootstrap sample mean. In chapter two we derive the simi-lar weak law of large numbers for the dependent bootstrap sample under the the samecondition.In chapter three, utilizing an existing result for identically distributed random vari-ables, and assuming that the moment of 1+δorder is finite, we derive the strong law oflarge numbers for the dependent bootstrap sample generated from identically distributedrandom variables, and therefore broaden the results which Smith and Taylor establishedfor i.i.d random variables.