Related papers: Confidence Bands for the Logistic and Probit Regre…
Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are nonstochastic. In practice, however, in order to improve finite…
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…
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.…
The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…
We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved…
We propose a method to quantify uncertainty around individual survival distribution estimates using right-censored data, compatible with any survival model. Unlike classical confidence intervals, the survival bands produced by this method…
Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the…
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…
Conformal prediction methods construct prediction regions for iid data that are valid in finite samples. We provide two parametric conformal prediction regions that are applicable for a wide class of continuous statistical models. This…
Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
Hard thresholding, LASSO , adaptive LASSO and SCAD point estimators have been suggested for use in the linear regression context when most of the components of the regression parameter vector are believed to be zero, a sparsity type of…
This research report outlines work, partially joint with Jeremy Kahn and Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal surfaces with boundary. One one hand, this lets us tell when one rubber band network is…
Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1,…
Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…
The density band model proposed by Kassam for robust hypothesis testing is revisited in this paper. First, a novel criterion for the general characterization of least favorable distributions is proposed, which unifies existing results. This…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…