Related papers: On adaptive inference and confidence bands
The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…
We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test…
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…
Let $f$ be a probability density and $C$ be an interval on which $f$ is bounded away from zero. By establishing the limiting distribution of the uniform error of the kernel estimates $f_n$ of $f$, Bickel and Rosenblatt (1973) provide…
Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…
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…
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…
Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the…
In epidemiology, some have argued that multiple comparison corrections are not necessary as there is rarely interest in the universal null hypothesis. From a parameter estimation perspective, epidemiologists may still be interested in…
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
We provide confidence bands for isotonic quantile curves in nonparametric univariate regression with guaranteed given coverage probability. The method is an adaptation of the confidence bands of Duembgen and Johns (2004) for isotonic median…
We show an essentially tight bound on the number of adaptively chosen statistical queries that a computationally efficient algorithm can answer accurately given $n$ samples from an unknown distribution. A statistical query asks for the…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
Most work on adaptive data analysis assumes that samples in the dataset are independent. When correlations are allowed, even the non-adaptive setting can become intractable, unless some structural constraints are imposed. To address this,…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…