Related papers: Adaptive Confidence Bands

Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…

We consider nonparametric regression in the context of functional data, that is, when a random sample of functions is observed on a fine grid. We obtain a functional asymptotic normality result allowing to build simultaneous confidence…

We consider a two-point correlator in massless $\phi^3$ model within the ladder approximation . The spectral density of the correlator is known explicitly and does not contain any resonances. Meanwhile making use of the standard sum rules…

Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as subsampling window width and…

We provide adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters when some of the nuisance parameters have known signs. The confidence intervals are adaptive in the sense that they tend to be short…

We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of three criteria can be simultaneously realized…

Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…

We propose a trust-region method for finite-sum minimization with an adaptive sample size adjustment technique, which is practical in the sense that it leads to a globally convergent method that shows strong performance empirically without…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

In this paper we establish asymptotic simultaneous confidence bands for the transformation kernel estimator of copulas introduced in Omelka et al.(2009). To this aim, we prove a uniform in bandwidth law of the iterated logarithm for the…

A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are…

In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…

This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…

The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…

We provide finite sample bounds on the Normal approximation to the law of the least squares estimator of the projection parameters normalized by the sandwich-based standard errors. Our results hold in the increasing dimension setting and…

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…

Penalized spline regression is a popular method for scatterplot smoothing, but there has long been a debate on how to construct confidence intervals for penalized spline fits. Due to the penalty, the fitted smooth curve is a biased estimate…

The frequency response function (FRF) is an established way to describe the outcome of experiments in posture control literature. The FRF is an empirical transfer function between an input stimulus and the induced body segment sway profile,…

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…

We establish a curvature estimate for classical minimal surfaces with total boundary curvature less than 4\pi. The main application is a bound on the genus of these surfaces depending solely on the geometry of the boundary curve. We also…