Assessing and Comparing the Applications of Bootstrap Methods

Assessing and Comparing the Applications of Bootstrap Methods Angela Zhu Mentor: John Kolassa, Department of Statistics and Biostatistics, Rutgers University

What is a Confidence Interval? n Given a point estimate of a population parameter, the confidence interval is an interval that likely contains the true value of the population parameter.

Bootstrapping A method for estimating or approximating the sampling distribution of a statistic. n Often considered a resampling procedure that employs numerical approximations. n Various techniques for computing confidence intervals using only the information contained in data sets. n

Bootstrapping Procedure n n n Take a sample of n elements from a population and compute statistic of interest. From the original sample, sample with replacement n elements—bootstrap sample. Compute the same statistic for each bootstrap sample. Take numerous bootstrap samples, say 1000, to obtain a bootstrap distribution of the statistic.

Bootstrap Methods Percentile n Residual n BCA n and various other procedures for making bootstrap confidence intervals. n

Purpose and Goals of Project n n Assess which bootstrapping methods perform well with respect to confidence interval coverage—want a coverage rate close to 95%. Plan: – Numerical survey of bootstrap approaches to various statistical estimators and different underlying distributions to assess and compare accuracy. – Perform simulations employing common distributions, such as the normal, exponential, and uniform distributions and evaluate their performances. – Consider research that has already been done in this area and make comparisons with our study.