On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean

1965/04/01 by Y. S. Chow, Herbert Robbins · 5 citations
Computer Science · Mathematics · Decision Sciences · #Bayesian Methods and Mixture Models #Statistical Methods and Inference #Probability and Risk Models

paper · doi:10.1214/aoms/1177700156

Abstract

Let x1, x2, • • • be a sequence of independent observations from some population. We want to find a confidence interval of prescribed width 2d and prescribed coverage probability a for the unknown mean µ of the population. If the variance σ2 of the population is known, and if d is small compared to σ 2, this can be done as follows. For any n ⪴ 1 define \(x_n = n ^{- 1}∑\nolimits₁ⁿ Xi,I_n = [ x_n - d,x_n + d ],\) and choose a to satisfy \(( 2π ) - ^1 \over 2∫ _{- a}^a e ^{- u2/2}du = a\)

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