Related papers: Optimal Confidence Bands for Shape-Restricted Curv…
In this paper, we propose and study construction of confidence bands for shape-constrained regression functions when the predictor is multivariate. In particular, we consider the continuous multidimensional white noise model given by $d…
Suppose that one observes pairs $(x_1,Y_1)$, $(x_2,Y_2)$, ..., $(x_n,Y_n)$, where $x_1\le x_2\le ... \le x_n$ are fixed numbers, and $Y_1,Y_2,...,Y_n$ are independent random variables with unknown distributions. The only assumption is that…
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…
We provide confidence bands for isotonic quantile curves in nonparametric univariate regression with guaranteed given coverage probability. The method is an adaptation of the confidence bands of Duembgen and Johns (2004) for isotonic median…
We observe a stochastic process $Y$ on $[0,1]^d$ ($d\geq 1$) satisfying $dY(t)=n^{1/2}f(t)dt$ + $dW(t)$, $t \in [0,1]^d$, where $n \geq 1$ is a given scale parameter (`sample size'), $W$ is the standard Brownian sheet on $[0,1]^d$ and $f…
Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-H\"older balls, $0<t\le r$, where $r$ is a…
Confidence bands are confidence sets for an unknown function f, containing all functions within some sup-norm distance of an estimator. In the density estimation, regression, and white noise models, we consider the problem of constructing…
The choice of hyperparameters greatly impacts performance in natural language processing. Often, it is hard to tell if a method is better than another or just better tuned. Tuning curves fix this ambiguity by accounting for tuning effort.…
Quantifying uncertainty using confidence regions is a central goal of statistical inference. Despite this, methodologies for confidence bands in Functional Data Analysis are still underdeveloped compared to estimation and hypothesis…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…
Uniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for…
Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable…
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…
We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f^\star which is close to, but simpler…
Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional…
This paper develops bootstrap methods to construct uniform confidence bands for nonparametric spectral estimation of L\'{e}vy densities under high-frequency observations. We assume that we observe $n$ discrete observations at frequency…
Conformal methods create prediction bands that control average coverage under no assumptions besides i.i.d. data. Besides average coverage, one might also desire to control conditional coverage, that is, coverage for every new testing…
We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multi-scale methods of testing and based on refined laws of the iterated logarithm for the normalized uniform…
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…