Related papers: Uniform Estimation Beyond the Mean

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…

Given an i.i.d. sample drawn from some probability distribution on a finite set, the best (in the sense of least variance) linear unbiased estimator (BLUE) of the average of any quantity with respect to that distribution is the sample…

This paper is devoted to establishing exponential bounds for the probabilities of deviation of a sample sum from its expectation, when the variables involved in the summation are obtained by sampling in a finite population according to a…

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…

This paper establishes the functional average as an important estimand for causal inference. The significance of the estimand lies in its robustness against traditional issues of confounding. We prove that this robustness holds even when…

Generalised regression estimation allows one to make use of available auxiliary information in survey sampling. We develop three types of generalised regression estimator when the auxiliary data cannot be matched perfectly to the sample…

Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…

Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to…

In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…

We propose the family of generalized resubstitution classifier error estimators based on empirical measures. These error estimators are computationally efficient and do not require re-training of classifiers. The plain resubstitution error…

Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…

In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this…

The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…

A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally $O(n^{-1/2})$ and can be very considerable when the distribution is heavily biased or…

Yang (1978) considered an empirical estimate of the mean residual life function on a fixed finite interval. She proved it to be strongly uniformly consistent and (when appropriately standardized) weakly convergent to a Gaussian process.…

Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…

Consider $n$ independent random numbers with a uniform distribution on $[0,1]$. The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is described by the Eulerian numbers. This is related to, but…

We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Hal\'asz. Several…