In this paper, we define the adaptive kernel estimation of the conditional distribution function (cdf) for independent and identically distributed (iid) data using varying bandwidth. The bias, variance and the mean squared error of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated.The results of the simulation study show that the adaptive kernel estimation of the conditional quantiles with varying bandwidth have better performance than the kernel estimations with fixed bandwidth.
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