Related papers: Mean skewness measures
In many scientific and data-driven applications, machine learning models are increasingly used as measurement instruments, rather than merely as predictors of predefined labels. When the measurement function is learned from data, the…
In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum…
Fr\'echet means are indispensable for nonparametric statistics on non-Euclidean spaces. For suitable random variables, in some sense, they "sense" topological and geometric structure. In particular, smeariness seems to indicate the presence…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
Importance-weighting is a popular and well-researched technique for dealing with sample selection bias and covariate shift. It has desirable characteristics such as unbiasedness, consistency and low computational complexity. However,…
Researchers often impute continuous variables under an assumption of normality, yet many incomplete variables are skewed. We find that imputing skewed continuous variables under a normal model can lead to bias; the bias is usually mild for…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering…
This paper proposes a new method for determining similarity and anomalies between time series, most practically effective in large collections of (likely related) time series, by measuring distances between structural breaks within such a…
Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness $D_3$ is bounded from…
Given a graph with node attributes, what neighborhoods are anomalous? To answer this question, one needs a quality score that utilizes both structure and attributes. Popular existing measures either quantify the structure only and ignore…
The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the…
This paper presents a new way to account for downside and upside risks when producing density nowcasts of GDP growth. The approach relies on modelling location, scale and shape common factors in real-time macroeconomic data. While movements…
Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the…
The adapted Wasserstein distance controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the adapted…