Sankhya: The Indian Journal of Statistics
1995, Volume 57, Series A, Pt. 1, pp. 100--117
ON FINE-TUNING A PURELY SEQUENTIAL PROCEDURE AND ASSOCIATED SECOND-ORDER PROPERTIES
NITIS MUKHOPADHYAY and SUJAY DATTA, University of Conncticut
SUMMARY. The idea of fine-tuning a purely sequential procedure in fairly general setup is persued so that when one provides the second-order expansion of some appropriate moment of the corresponding stopping variable, one obtains the limiting value as the leading term followed only by a remainder that has the same order as that of the original, that is pre-fine-tuned, methodology. First, we provide a general result that gives an explicit expression for the fine-tuning factor, followed by the examples to show the improvement in the coverage accuracy of a few sequential fixed-size confidence region problems. the paper includes (i) univariate and multivariate estimation problems, (ii) linear regression problems, (iii) selection and ranking problems, and (iv) ordered parameter estimationproblems. Brief moderate sample comparisons of the original and fine-tuned versions are also indicated for some multivariate sequential estimation techniques.
AMS (1990) subject classification. 62L12, 62L99, 62F07.
Key words and phrases. Purely sequential procedure, fine-tuning factor, second-order expansions, fixed-size confidence regions, bounded risk point estimation, linear regression, multivariate problems, selection and ranking, ordered parameter estimation.
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