Methods for Estimating a Conditional Distribution Function

Minimax estimation of the conditional cumulative distribution function

“…But we cannot handle the context where Y and C are independent only conditionally on X, whereas Beran's or Stute's estimators capture this case. Some other ideas were later developed by Li and Doss (1995) and Hall, Wolff and Yao (1999). First, Li and Doss (1995) present nonparametric methods which are very powerful but lack of adaptivity w.r.t.…”

“…the conditioning variable. On the other hand, Hall et al (1999) discuss local linear methods and methods for which the conditional c.d.f. estimator is constrained to lie between 0 and 1 and to be monotone increasing, a property which is also satisfied by our estimator by a post-processing.…”

“…Hall et al (1999) The sets A = A 1 × A 2 are fixed intervals, roughly calibrated with respect to each distribution. In practice, we would have chosen the compact sets of estimation with respect to the data (and their extreme values).…”

Nonparametric estimation of conditional VaR and expected shortfall

“…Here we need to mention that the boundary effect might cause a problem for estimating ν p (x) since it only concerns the tail probability. So, Hall et al (1999) and Cai (2002) proposed the WNW estimator, which is designed to possess the superior properties of local linear method and to preserve the property that the NW estimator is always a distribution function. The WNW estimator of…”

Measuring intra-distribution income dynamics: an application to the European regions

“…Small bandwidths produce small bias and large variance, while large bandwidths yield large bias and small variance. 9 These authors proposed a three-step strategy for bandwidth selection: first, bandwidth selection with the traditional rule suggested bySilverman (1986); second, a bootstrap bandwidth selection approach for estimating conditional distribution functions(Hall et al 1999); third, a regression-based bandwidth selector(Fan et al 1996).…”