NONPARAMETRIC SEQUENTIAL CONFIDENCE ESTIMATION BY FIXED-WIDTH CONFIDENCE INTERVALS: ASYMPTOTIC CONSISTENCY AND ASYMPTOTIC EFFICIENCY
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https://doi.org/10.5281/zenodo.18168670##article.subject##:
random variable, stopping time, confidence interval, fixed width, asymptotic consistency, asymptotic efficiency, probability density, linear random process.##article.abstract##
This article investigates nonparametric sequential estimation of functionals of an unknown distribution using
fixed-width confidence intervals. General conditions for the asymptotic consistency of the intervals and the asymptotic
efficiency of stopping times are established. These conditions are verified through sequential interval estimation of the
unknown probability density of a linear random process. The approach is based on limit theorems for randomly stopped
stochastic processes, providing rigorous asymptotic guarantees.
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