A Comparison of Various Approaches to Sequential Estimation in an Errors-in-variables Model

• Activity Number: 285
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Sujay Datta*+
• Affiliation(s): Northern Michigan University
• Keywords: measurement-error models ; errors-in-variables models ; structural relationship ; sequential estimation ; second-order asymptotics ; simulation studies

Abstract

An errors-in-variables (EIV) model, also known as a measurement-error model, has been widely discussed in the literature. See, for example, Anderson (1984, Annals of Statistics), Gleser (1981, Annals of Statistics), or Fuller's book (1987, Wiley). For a "structural relationship" model with two variables x and y (both measures with errors), it has been shown that the coverage prob. of any finite-width interval for the slope constructed via a fixed sample-size procedure decreases to zero as a certain variance-ratio approaches zero. Even a multistage procedure with a finite number of steps (e.g., two-stage, three-stage) does not improve the situation. Here we address the problem of constructing a fixed-width confidence interval for the slope via a sequential (one-at-a-time) sampling scheme. We consider three different approaches leading to three different stopping rules, and compare their performances (i.e., average sample sizes and resulting coverage probs) through simulation studies. Then, we briefly indicate how to derive the asymptotic second-order properties of one of the procedures (similar derivations for the other ones have yet to be done).Finally, we show an application on a data-set.