Accounting For Variability Due To Resampling Using Bootstrapping

Summer 2024

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Charles Champ

Andrew Sills

Divine Wanduku

Abstract

Bradley Efron (1979) introduced bootrapping. Typically a researcher is interested in studying a process which generates individuals. The collection of individuals the process has(actual) or could have (conceptual) generated is the population. The collection of conceptual members of the population is an uncountable collection. Hence, the population is anuncountable collection of individuals. The collection of individuals the process has generated (actual individuals) is representative of what the process can generate and will bereferred to as the representative sample. The size of this sample is a nonnegative integervalued random variable N which may be a constant random variable such as in statistically designed experiments in which the researcher decides the value of N before collecting thedata. In general, the variable N is a random variable N whose value is generated by the process. We note that in the design of experiments the researcher becomes a part of the processthat generates “actual” individuals in the population. There is variability that must be accounted for among the measurement on the individuals in the representative sample. Fromthe representative sample, the researcher using a sampling method will select a sample referred to as the researcher’s sample. There is variability of among the measurements that must be accounted for in the researcher’s sample. A bootstrap sample introduces furthervariability that must be accounted for. We will study bootstrapping in which we account for the variability in the bootstrap sample.

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