Conditional Empirical Processes Defined by Nonstationary Absolutely Regular Sequences

K. I. Yoshihara (1990,Comput. Math. Appl.19, No. 1, 149–158) proved the weak invariance of the conditional nearest neighbor regression function estimator called the conditional empirical process based onϕ-mixing observations. In this paper, we extend the result for nonstationary and absolutely regular random variables which have applications for Markov processes, for which the initial measure is not necessary, the invariant measure.