Related papers: Quantile processes and their applications in finit…
We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…
Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying…
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…
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To…
This paper studies the propagation of finite-sample uncertainty under nonlinear transformations commonly used in statistical decision systems. In particular, we consider process capability indices, which are widely used in manufacturing…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
In modern data analysis, it is common to select a model before performing statistical inference. Selective inference tools make adjustments for the model selection process in order to ensure reliable inference post selection. In this paper,…
As generative AI models are increasingly used to simulate real-world systems, quantifying the ``sim-to-real'' gap is critical. For each input setting of interest -- which we call a \emph{scenario}, such as a survey question or operating…
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…
We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
The delta method creates more general inference results when coupled with central limit theorem results for the finite population. This opens up a range of new estimators for which we can find finite population asymptotic properties. We…
Parameters of sub-populations can be more relevant than super-population ones. For example, a healthcare provider may be interested in the effect of a treatment plan for a specific subset of their patients; policymakers may be concerned…
The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity…