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Let $ {(X_i, Y_i) : i = 1, 2, ldots } $ be a sequence of stationary independent random vectors in $ Re^{(2)} $ with a continuous distribution, and let $ G_x(cdot) $ denote the conditional distribution... function of $ Y_1 $ given $ X_1 = x $. In this paper, Bahadur's almost sure representation for the sample conditional quantile $ hat{G}_{nx}^{-1} $, $ 0 < lambda <1 $, is established, where $ hat{G}_{nx} $, is a smoothed (rank nearest neighbor or the Nadaraya-Watson type) estimator of $ hat{G}_{nx} $. Such representations arc useful in the study of asymptotics of functionals of conditional quantiles.show more
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