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Sequential Nonparametric Fixed-Width Confidence Intervals for Conditional Quantiles
Journal article   Peer reviewed

Sequential Nonparametric Fixed-Width Confidence Intervals for Conditional Quantiles

S. C. Bagui, K. L. Mehra and Y. S. Rama Krishnaiah
Sequential analysis, Vol.29(1), pp.69-87
01/2010
DOI: https://doi.org/10.1080/07474940903482429

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Abstract

Let {(X i , Y i ): i ≥ 1} be a sequence of bivariate r.v.'s from a continuous distribution H with marginals F and G, respectively, and let Gx(·) denote the conditional distribution of Y 1 given X 1 = x, x ∊ Λ(F), the support of F. In this paper sequential fixed-width confidence interval procedures of length (at most) 2d for the conditional quantile q x (λ) = inf {y: G x (y) ≥ λ}, 0 < λ <1, are studied based on sample conditional quantiles, where G*nx(·) denotes a 'smoothed' or 'unsmoothed' rank nearest neighbor or Nadaraya-Watson-type kernel estimator of Gx(·). Asymptotics of these sequential confidence interval procedures including their consistency and (relative) efficiency properties are studied, as d → 0, on the lines of Chow and Robbins (1965), Geertsema (1970), and Stute (1983). The relative efficiencies and deficiencies of these procedures with respect to each other along with some supportive Monte Carlo results are also presented.

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