Related papers: Simple and Honest Confidence Intervals in Nonparam…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data…
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…
Inference methods for computing confidence intervals in parametric settings usually rely on consistent estimators of the parameter of interest. However, it may be computationally and/or analytically burdensome to obtain such estimators in…
To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the…
We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…
We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a…
We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the…
The US Census Bureau will deliberately corrupt data sets derived from the 2020 US Census, enhancing the privacy of respondents while potentially reducing the precision of economic analysis. To investigate whether this trade-off is…
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…
Consider the nonparametric regression model Y=m(X)+E, where the function m is smooth but unknown, and E is independent of X. An estimator of the density of the error term E is proposed and its weak consistency is obtained. The contribution…
Various methods have recently been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data generating processes when high-dimensional nuisance models are estimated by post-model-selection or…
Matching algorithms are commonly used to predict matches between items in a collection. For example, in 1:1 face verification, a matching algorithm predicts whether two face images depict the same person. Accurately assessing the…
We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…
This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local…
The recent decade has seen an enormous rise in the popularity of deep learning and neural networks. These algorithms have broken many previous records and achieved remarkable results. Their outstanding performance has significantly sped up…
Vertically weighted averages perform a bilateral filtering of data, in order to preserve fine details of the underlying signal, especially discontinuities such as jumps (in dimension one) or edges (in dimension two). In homogeneous regions…
The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of…
Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null…
In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training…