Related papers: A sharp adaptive confidence ball for self-similar …
One-sided confidence intervals are presented for the average of non-identical Bernoulli parameters. These confidence intervals are expressed as analytical functions of the total number of Bernoulli games won, the number of rounds and the…
In high-dimensional linear models the problem of constructing adaptive confidence sets for the full parameter is known to be generally impossible. We propose re-weighted loss functions under which constructing fully adaptive confidence sets…
Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this work, for the first time, we apply conformal-prediction to…
This paper revisits the simple, but empirically salient, problem of inference on a real-valued parameter that is partially identified through upper and lower bounds with asymptotically normal estimators. A simple confidence interval is…
In this paper, we investigate optimal linear approximations ($n$-approximation numbers ) of the embeddings from the Sobolev spaces $H^r\ (r>0)$ for various equivalent norms and the Gevrey type spaces $G^{\alpha,\beta}\ (\alpha,\beta>0)$ on…
A confidence sequence (CS) is an anytime-valid sequential inference primitive which produces an adapted sequence of sets for a predictable parameter sequence with a time-uniform coverage guarantee. This work constructs a non-parametric…
For any compact surface $\Sigma$ with smooth, non-empty boundary, we construct a free boundary minimal immersion into a Euclidean Ball $\mathbb{B}^N$ where $N$ is controlled in terms of the topology of $\Sigma$. We obtain these as…
It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…
Estimating the conditional mean function is a central task in statistical learning. In this paper, we consider estimation and inference for a nonparametric class of real-valued cadlag functions with bounded sectional variation (Gill et al.,…
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…
We study a variant of the median problem for a collection of point sets in high dimensions. This generalizes the geometric median as well as the (probabilistic) smallest enclosing ball (pSEB) problems. Our main objective and motivation is…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
Within the nonparametric regression model with unknown regression function $l$ and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis $l=0$ against a…
Estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with (very) large samples of high dimensional data. The collected data may be contaminated by noise so that robust…
We reveal the phenomenon that ``naive'' multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal convergence rate for nonparametric estimation of regression…
Counterfactual explanations offer an intuitive and straightforward way to explain black-box models and offer algorithmic recourse to individuals. To address the need for plausible explanations, existing work has primarily relied on…
This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of…
This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…