Date Thesis Awarded
Honors Thesis -- Open Access
Bachelors of Science (BS)
Let X1, X2, . . . , Xn be independent and identically distributed Bernoulli(p) random variables with unknown parameter p satisfying 0 < p < 1. Let X = Pn i=1 Xi be the number of successes in the n mutually independent Bernoulli trials. The maximum likelihood estimator of p is ˆp = X/n. For fixed n and α, there are n + 1 distinct 100(1 − α)% confidence intervals associated with X = 0, 1, 2, . . . , n. Currently there is no known exact confidence interval for p. Our goal is to construct the confidence interval for p whose actual coverage is closest to the stated coverage, using the root mean squared error, RMSE, to measure the difference between the actual coverage and the stated coverage. The approximate confidence interval for p developed here minimizes the RMSE for a sample size n and a significance level α.
Feng, Kexin, "RMSE-Minimizing Confidence Intervals for the Binomial Parameter" (2020). Undergraduate Honors Theses. William & Mary. Paper 1456.
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