Related papers: Confidence bands for densities, logarithmic point …
To evaluate a classification algorithm, it is common practice to plot the ROC curve using test data. However, the inherent randomness in the test data can undermine our confidence in the conclusions drawn from the ROC curve, necessitating…
A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. Our work develops confidence sequences whose widths go to zero, with nonasymptotic coverage guarantees under nonparametric…
In this paper we develop procedures to construct simultaneous confidence bands for $\tilde p$ potentially infinite-dimensional parameters after model selection for general moment condition models where $\tilde p$ is potentially much larger…
Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding's inequality that use…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
We consider nonparametric regression in the context of functional data, that is, when a random sample of functions is observed on a fine grid. We obtain a functional asymptotic normality result allowing to build simultaneous confidence…
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…
The bootstrap is a popular method of constructing confidence intervals due to its ease of use and broad applicability. Theoretical properties of bootstrap procedures have been established in a variety of settings. However, there is limited…
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected…
In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…
Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
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.…
We propose a methodology for constructing confidence regions with partially identified models of general form. The region is obtained by inverting a test of internal consistency of the econometric structure. We develop a dilation bootstrap…
In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…
In Mombeni et al. (2019), Birnbaum-Saunders and Weibull kernel estimators were introduced for the estimation of cumulative distribution functions (c.d.f.s) supported on the half-line $[0,\infty)$. They were the first authors to use…
Interval estimation of quantiles has been treated by many in the literature. However, to the best of our knowledge there has been no consideration for interval estimation when the data are available in grouped format. Motivated by this, we…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
We prove the asymptotic normality of the kernel density estimator (introduced by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly mixing random fields. Our approach is based on the Lindeberg's method rather than on…
Considering a determinantal point process on the real line, we establish a connection between the sine-kernel asymptotics for the correlation kernel and the CLT for mesoscopic linear statistics. This implies universality of mesoscopic…