Related papers: Precise quantile function estimation from the char…

We present on-line algorithms for computing approximations of rank-based statistics that give high accuracy, particularly near the tails of a distribution, with very small sketches. Notably, the method allows a quantile $q$ to be computed…

Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control…

Quantile regression provides a consistent approach to investigating the association between covariates and various aspects of the distribution of the response beyond the mean. When the regression covariates are measured with errors,…

As data volume grows extensively, data profiling helps to extract metadata of large-scale data. However, one kind of metadata, order statistics, is difficult to be computed because they are not mergeable or incremental. Thus, the limitation…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the…

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…

Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…

Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…

Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…

In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…

Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of…

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms…

A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…