Related papers: Confidence Sets under Generalized Self-Concordance
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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…
We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero…
We consider the problem of estimating small ball probabilities $\mathbb P\{f(G) \leqslant \delta \mathbb Ef(G)\}$ for sub-additive,positively homogeneous functions $f$ with respect to the Gaussian measure. We establish estimates that depend…
We study the support recovery problem for a high-dimensional signal observed with additive noise. With suitable parametrization of the signal sparsity and magnitude of its non-zero components, we characterize a phase-transition phenomenon…
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference…
Constructing nonasymptotic confidence intervals (CIs) for the mean of a univariate distribution from independent and identically distributed (i.i.d.) observations is a fundamental task in statistics. For bounded observations, a classical…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
The problem of identifying statistically significant inferences about the structure of the graphical model is considered, along with the related task of constructing a confidence set for a graphical model. It has been proven that the…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
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…
Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…
We build confidence balls for the common density $s$ of a real valued sample $X_1,...,X_n$. We use resampling methods to estimate the projection of $s$ onto finite dimensional linear spaces and a model selection procedure to choose an…
Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size $n$ and $d$ tend to infinity. We achieve…