Related papers: Optimal Confidence Bands for Shape-Restricted Curv…
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,…
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…
Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many…
We consider the problem of constructing Bayesian based confidence sets for linear functionals in the inverse Gaussian white noise model. We work with a scale of Gaussian priors indexed by a regularity hyper-parameter and apply the…
We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares…
To evaluate a classification algorithm, it is common practice to plot the ROC curve using test data. However, the inherent randomness in the test data can undermine our confidence in the conclusions drawn from the ROC curve, necessitating…
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…
Confidence sets from i.i.d. data are constructed for the extrinsic mean of a probabilty measure P on spheres, real projective spaces, and complex projective spaces, as well as Grassmann manifolds, with the latter three embedded by the…
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected…
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…
A priori bound for the parameter to be estimated is incorporated into confidence intervals within frequentistic approach in a straightforward and optimal fashion, ensuring the best resolution of non-boundary values as well as robustness for…
The paper introduces a method to construct confidence bands for bounded, band-limited functions based on a finite sample of input-output pairs. The approach is distribution-free w.r.t. the observation noises and only the knowledge of the…
In this paper we study the problem of constructing bootstrap confidence intervals for the L\'evy density of the driving L\'evy process based on high-frequency observations of a L\'evy-driven moving average processes. Using a spectral…
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…
A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the proposed confidence set enjoys uniform coverage over all non-decreasing regression functions.…
In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…
Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…
This paper develops a simple method to construct confidence bands, centered at a principal component analysis (PCA) based estimator, for the slope function in a functional linear regression model with a scalar response variable and a…
We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d.~observations. Our approach…
Ordinary differential equation (ODE) is an important tool to study the dynamics of a system of biological and physical processes. A central question in ODE modeling is to infer the significance of individual regulatory effect of one signal…