Related papers: Confidence bands for convex median curves using si…
Let $Y$ be a stochastic process on $[0,1]$ satisfying $dY(t) = n^{1/2} f(t) dt + dW(t)$, where $n \ge 1$ is a given scale parameter (``sample size''), $W$ is standard Brownian motion and $f$ is an unknown function. Utilizing suitable…
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…
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…
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…
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…
Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the…
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.…
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 develops a method to construct uniform confidence bands for a nonparametric regression function where a predictor variable is subject to a measurement error. We allow for the distribution of the measurement error to be unknown,…
Ratio of medians or other suitable quantiles of two distributions is widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated cross-sectional data are…
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…
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…
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…
We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to…
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…
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 construct uniform and point-wise asymptotic confidence sets for the single edge in an otherwise smooth image function which are based on rotated differences of two one-sided kernel estimators. Using methods from M-estimation, we show…
The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…
This article presents methods for the construction of two-sided and one-sided simultaneous hyperbolic bands for the logistic and probit regression models when the predictor variable is restricted to a given interval. The bands are…