Related papers: A simple approach to construct confidence bands fo…
Let $f$ be a probability density and $C$ be an interval on which $f$ is bounded away from zero. By establishing the limiting distribution of the uniform error of the kernel estimates $f_n$ of $f$, Bickel and Rosenblatt (1973) provide…
This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…
We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine…
We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…
We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
Conformal inference is a versatile tool for building prediction sets in regression or classification. We study the false coverage proportion (FCP) in a simultaneous inference setting with a calibration sample of $n$ points and a test sample…
Regression modeling is the workhorse of statistics and there is a vast literature on estimation of the regression function. It is realized in recent years that in regression analysis the ultimate aim may be the estimation of a level set of…
In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…
Sample autocorrelograms typically come with significance bands (non-rejection regions) for the null hypothesis of no temporal correlation. These bands have two shortcomings. First, they build on pointwise intervals and suffer from joint…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property called conditional coverage. A typical approach to this task is to estimate the conditional…
We propose a method to quantify uncertainty around individual survival distribution estimates using right-censored data, compatible with any survival model. Unlike classical confidence intervals, the survival bands produced by this method…
Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly…
Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. This article develops a continuous threshold expectile regression for modeling data in which…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…