Yoshihara, Ken-ichi Bahadur-type representation of sample conditional quantiles based on weakly dependent data. (English) Zbl 0798.62067 Yokohama Math. J. 41, No. 1, 51-66 (1993). Let \(\{(X_ i,Z_ i)\}\) be a strictly stationary sequence of two- dimensional random vectors defined on a probability space \((\Omega, {\mathcal F}, P)\). For \(0<p<1\), let \(\theta_ p (x)\) denote the \(p\)-quantile of \(Z\) given \(X=x\). P. K. Bhattacharya and A. K. Gangopadhyay [Ann. Stat. 18, No. 3, 1400-1415 (1990; Zbl 0706.62040)] obtained Bahadur type representations of nearest neighbor and kernel estimators of \(\theta_ p(x)\) when \(\{(X_ i,Z_ i)\}\) are independent and identically distributed random vectors. In this paper the author considers the analogous problem when \(\{(X_ i,Z_ i)\}\) satisfies some mixing condition. Reviewer: A.Földes (Staten Island) MSC: 62G20 Asymptotic properties of nonparametric inference 62G05 Nonparametric estimation 62G30 Order statistics; empirical distribution functions 60F15 Strong limit theorems Keywords:absolutely regular; conditional quantile; conditional absolute regularity; conditional phi-mixing; nearest-neighbor estimator; order statistics; induced order statistics; weakly dependent data; strictly stationary sequence of two-dimensional random vectors; Bahadur type representations; kernel estimators Citations:Zbl 0706.62040 PDFBibTeX XMLCite \textit{K.-i. Yoshihara}, Yokohama Math. J. 41, No. 1, 51--66 (1993; Zbl 0798.62067)