Abstract
The purely sequential sampling procedure proposed by Mukhopadhyay and Abid (1986) is customarily used to construct a fixed-size confidence region for regression parameters. This methodology has asymptotic efficiency and asymptotic consistency properties, but it does not have the exact consistency property. We propose that sequential sampling be continued allowing the sample size to cross a corresponding boundary multiple times. The asymptotic efficiency and asymptotic consistency properties are ascertained for multiple crossing stopping rules (Theorem 2.1). A truncation technique as well as a fine-tuning adjustment are developed. The simulated data are generated by realistic models arising from a study that investigates the association between prostate-specific antigen (PSA) and a number of appropriate prognostic clinical covariates. We highlight via large-scale simulations the remarkable gain in nearly achieving the target coverage without significant over-sampling. DOI: http://dx.doi.org/10.4038/sljastats.v5i4.7789
Highlights
Multi-stage sampling designs date back to Mahalanobis (1940)
The sequential methodology is governed by multiple crossing stopping rules, originally developed by Mukhopadhyay and Muthu Poruthotage (2013,2014) and Muthu Poruthotage (2013) in the context of fixed-size confidence regions for a normal mean
We broaden the notion of multiple crossing by addressing fixed-size regression parameter estimation problems
Summary
Multi-stage sampling designs date back to Mahalanobis (1940). Stein’s (1945) and Wald’s (1947) methodological breakthroughs highlighted the importance of multi-stage and sequential sampling designs. Multi-stage and sequential sampling methodologies were developed for point estimation, interval estimation, hypothesis testing, selection and ranking, and other problems in inference. We implement a new sequential sampling methodology to construct fixedsize confidence regions for regression parameters with a prespecified confidence coefficient. The sequential methodology is governed by multiple crossing stopping rules, originally developed by Mukhopadhyay and Muthu Poruthotage (2013,2014) and Muthu Poruthotage (2013) in the context of fixed-size confidence regions for a normal mean. We broaden the notion of multiple crossing by addressing fixed-size regression parameter estimation problems
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