Related papers: A new definition of nonlinear statistics mean and …
This paper considers a nonlinear quantile model with change-points. The quantile estimation method, which as a particular case includes median model, is more robust with respect to other traditional methods when model errors contain…
We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a…
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
In this paper, a novel statistical metric learning is developed for spectral-spatial classification of the hyperspectral image. First, the standard variance of the samples of each class in each batch is used to decrease the intra-class…
We present an axiomatic approach to the mean and discuss generalizations of the mean, including one due to Kolmogorov based on the Weak Law of Large Numbers. We offer examples and counterexamples, describe conventional and unconventional…
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…
The odds ratio measure is used in health and social surveys where the odds of a certain event is to be compared between two populations. It is defined using logistic regression, and requires that data from surveys are accompanied by their…
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This paper considers the problem of estimating the variance of a sum of a triangular array of random vectors with heterogeneous means. When random vectors exhibit two-way cluster dependence or weak dependence, standard variance estimators…
Classical measures of inequality use the mean as the benchmark of economic dispersion. They are not sensitive to inequality at the left tail of the distribution, where it would matter most. This paper presents a new inequality measurement…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
New procedures for detecting a change in the cross-sectional mean of panel data are proposed. The procedures rely on estimating nuisance parameters using certain cross-sectional means across panels using a weighted least squares regression.…
This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…
For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…