Related papers: Reduction principles for quantile and Bahadur-Kief…
Linear quantile regression models aim at providing a detailed and robust picture of the (conditional) response distribution as function of a set of observed covariates. Longitudinal data represent an interesting field of application of such…
In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to…
In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform…
The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change…
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…
We consider multivariate copula-based stationary time-series under Gaussian subordination. Observed time series are subordinated to long-range dependent Gaussian processes and characterized by arbitrary marginal copula distributions. First…
In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller…
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…
Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency…
Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those…
In this paper we establish the Bahadur-Kiefer representation for sample quantiles of GARCH sequences with optimal rates.
We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric…
Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing…
U-quantiles are applied in robust statistics, like the Hodges-Lehmann estimator of location for example. They have been analyzed in the case of independent random variables with the help of a generalized Bahadur representation. Our main aim…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver…
Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile…