相关论文: Asymmetric Errors
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
I present a critique of the methods used in a typical paper. This leads to three broad conclusions about the conventional use of statistical methods. First, results are often reported in an unnecessarily obscure manner. Second, the null…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
The basic statistical methods of data representation did not change since their emergence. Their simplicity was dictated by the intricacies of computations in the before computers epoch. It turns out that such approach is not uniquely…
Bell's inequalities can be understood in three different ways depending on whether the numbers featuring in the inequalities are interpreted as classical probabilities, classical conditional probabilities, or quantum probabilities. In the…
How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…
Long-range ensemble forecasts are typically verified as anomalies with respect to a lead-time dependent climatological mean to remove the influence of systematic biases. However, common methods for calculating anomalies result in…
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…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…
Statistical matching is a technique for integrating two or more data sets when information available for matching records for individual participants across data sets is incomplete. Statistical matching can be viewed as a missing data…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
A scientific phenomenon under study may often be manifested by data arising from processes, i.e. sources, that may describe this phenomenon. In this contex of multi-source data, we define the "out-of-source" error, that is the error…
Science students must deal with the errors inherent to all physical measurements and be conscious of the necessity to express their as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic.…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
In empirical work it is common to estimate parameters of models and report associated standard errors that account for "clustering" of units, where clusters are defined by factors such as geography. Clustering adjustments are typically…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…