Adaptive sequential confidence intervals for A location Parameter

Abstract

Let θ + X₁, θ + X₂... be a random sample and X_i's have a common distribution function F, where F has an absolutely continuous density f that is symmetric about origin. For a given confidence coefficient, a fully sequential procedure is proposed for constructing a fixed-width confidence interval for the location parameter θ. The result is based on Stone's (1975) adaptive maximum likelihood estimator. under mild conditions the procedure is shown to be asymptotically consistent and fully efficient.

Keywords:

• Fixed-width confidence interval
• asymptotic consistency
• asymptotic efficiency
• two-stage procedure
• adaptive estimation