Asymptotic expansions for sequential confidence levels in inverse linear regression

Abstract

Non-linear renewal theory is used to derive second order asymptotic expansions for the coverage probability of a fixed-width sequential confidence interval for an unknown parameter xin the inverse linear regression model. These expansions are obtained for a two-stage sequential procedure, proposed by Perng and Tong (1974) for the construction of a confidence interval for x.

Keywords:

• inverse linear regression
• fixed-width confidence intervals
• two-stage sequential procedure
• asymptotic expansions
• excess over the boundary