Non-Crossing Non-Parametric Estimates of Quantile Curves

Abstract

In this paper a new nonparametric estimate of conditional quantiles is proposed, that

Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression

“…However, as the conditional quantiles at different levels α 1 and α 2 are estimated independently it can occur that for given covariate realizations and levels α 1 < α 2 , q α 1 can have a larger value than q α 2 , an effect known as quantile crossing. Whereas different approaches have already been proposed to combat quantile crossing, see, e.g., He (1997), Dette and Volgushev (2008) or Bondell et al (2010), the novel D-vine copula based quantile regression of Kraus and Czado (2017a) also ensures that this effect is prevented.…”

Testing for additivity in nonparametric quantile regression

“…Dette and Volgushev (2008) demonstrate that the choice of the distribution function G has a negligible impact on the quality of the resulting estimate provided that an obvious centering and standardization is performed. Similarly, the estimateQ l,N (τ |x) is robust with respect to the choice of the bandwidth b n if it is chosen sufficiently small [see Dette et al (2006)].…”

“…Throughout this paper we denote by G : R → [0, 1] a strictly increasing given distribution function, which can be specified by the data analyst and denote by K a further positive one-dimensional kernel with compact support, say [−1, 1] with corresponding bandwidth b n . Following Dette and Volgushev (2008) we define…”

“…Most of the literature refers to models with a univariate predictor [see e.g. Yu and Jones (1997), Yu and Jones (1998), Dette and Volgushev (2008) and Chernozhukov et al (2010)]. While from a theoretical point of view there is no difficulty to generalize this methodology to high-dimensional covariates, it is well known that in practical applications such nonparametric methods suffer from the curse of dimensionality and therefore do not yield precise estimates of conditional quantile surfaces for reasonable sample sizes.…”

Testing Equality of Nonparametric Quantile Regression Functions

“…Therefore, an efficient nonparametric estimator of the common quantile regression function g τ (·) can be constructed by pooling the data from all groups. For independent data, several nonparametric quantile regression function estimators are available in the literature (Yu & Jones, 1998;Takeuchi, Le, Sears, & Smola, 2006;Dette & Volgushev, 2008;Bondell, Reich, & Wang, 2010). In this paper we use the local linear nonparametric quantile regression function estimator proposed by Yu and Jones (1998).…”