Related papers: Optimal Confidence Bands for Shape-Restricted Curv…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…
A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing…
Estimation of the complete distribution of a random variable is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting…
In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…
We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by…
Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…
We construct a canonical geometric rough path over $d$-dimensional tempered fractional Brownian motion (tfBm) for any Hurst parameter $H > 1/4$ and tempering parameter $\lambda > 0$. The main challenge stems from the non-homogeneous nature…
We obtain bounds for probabilities of deviations of the truncated variation functional of fractional Brownian motions (fBm) of any Hurst index $H \in (0,1)$ from their expected values. Obtained bounds are optimal for large values of…
We address the problem of optimizing a Brownian motion. We consider a (random) realization $W$ of a Brownian motion with input space in $[0,1]$. Given $W$, our goal is to return an $\epsilon$-approximation of its maximum using the smallest…
Given a fixed-sample-size test that controls the error probabilities under two specific, but arbitrary, distributions, a 3-stage and two 4-stage tests are proposed and analyzed. For each of them, a novel, concrete, non-asymptotic,…
In this paper, we propose an abstract procedure for debiasing constrained or regularized potentially high-dimensional linear models. It is elementary to show that the proposed procedure can produce $\frac{1}{\sqrt{n}}$-confidence intervals…
In this paper we introduce a new methodology to determine an optimal coefficient of penalized functional regression. We assume the dependent, independent variables and the regression coefficients are functions of time and error dynamics…
This paper investigates the size performance of Wald tests for CAViaR models (Engle and Manganelli, 2004). We find that the usual estimation strategy on test statistics yields inaccuracies. Indeed, we show that existing density estimation…
Expected coverage and expected length of 90% upper and lower limit and 68.27% central intervals are plotted as functions of the true signal for various values of expected background. Results for several objective priors are shown, and…
Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…
Confidence bounds are an essential tool for rigorously quantifying the uncertainty of predictions. They are a core component in many sequential learning and decision-making algorithms, with tighter confidence bounds giving rise to…
In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the…
We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…