相关论文: Asymmetric Errors
The presence of measurement error is a widespread issue which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Large-scale data analysis poses both statistical and computational problems which need to be addressed simultaneously. A solution is often straightforward if the data are homogeneous: one can use classical ideas of subsampling and mean…
Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…
Matched case-control studies are commonly employed in epidemiological research for their convenience and efficiency. Analysis of secondary outcomes can yield valuable insights into biological pathways and help identify genetic variants of…
This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…
Assessing uncertainty is an important step towards ensuring the safety and reliability of machine learning systems. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e.g. when the data…
We consider the setting of an aggregate data meta-analysis of a continuous outcome of interest. When the distribution of the outcome is skewed, it is often the case that some primary studies report the sample mean and standard deviation of…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…
A new approach to the problem of error correction in communication channels is proposed, in which the input sequence is transformed in such a way that the interdependence of symbols is significantly increased. Then, after the sequence is…
This review article considers some of the most common methods used in astronomy for regressing one quantity against another in order to estimate the model parameters or to predict an observationally expensive quantity using trends between…
Statistical matching is an effective method for estimating causal effects in which treated units are paired with control units with ``similar'' values of confounding covariates prior to performing estimation. In this way, matching helps…
Various measures can be used to estimate bias or unfairness in a predictor. Previous work has already established that some of these measures are incompatible with each other. Here we show that, when groups differ in prevalence of the…
A method is presented for using the consistent part of inconsistent axiomatic systems.
Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.