Small Sample Theory for Steady State Confidence Intervals
Abstract
The goal of this dissertation is to develop a nonparametric method for obtaining a confidence interval for the mean of a stationary sequence. As indicated in the literature, nonparametric confidence intervals in practice often have undesirable small-sample asymmetry and coverage characteristics. These phenomena are partially due to the fact that the third and fourth cumulants of the point estimator for the stationary mean, unlike those of the standard normal random variable, are not zero. We will apply Edgeworth and Cornish-Fisher expansions to obtain asymptotic expansions for the errors associated with confidence intervals. The analysis isolates various elements that contribute to errors and makes it possible for us to estimate each element and hopefully correct the errors to a smaller order. We will use Glynn's method to develop first and second order pivots for the confidence intervals. Furthermore, these procedures also improve the asymptotic order of confidence interval accuracy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1989
- Accession Number
- ADA212097
Entities
People
- Chia-hon Chien
Organizations
- Stanford University