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Asymptotic consistency of fixed-width sequential confidence intervals for a multiple regression function

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Summary

Letm n (x) be the recursive kernel estimator of the multiple regression functionm(x)=E[Y|X=x]. For given α (0<α<1) andd>0 we define a certain class of stopping timesN=N(α,d, x) and takeI N,d (x)=[m N (x)−d, m N (x)+d] as a 2d-width confidence interval form(x) at a given pointx. In this paper it is shown that the probability P{m(x)∈I N,d (x)} converges to α asd tends to zero.

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Authors and Affiliations

  1. Niigata University, Niigata, Japan

    Eiichi Isogai

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  1. Eiichi Isogai
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Isogai, E. Asymptotic consistency of fixed-width sequential confidence intervals for a multiple regression function. Ann Inst Stat Math 38, 69–83 (1986). https://doi.org/10.1007/BF02482501

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  • DOI: https://doi.org/10.1007/BF02482501

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