Related papers: A few properties of sample variance

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…

We consider a problem of statistical mean estimation in which the samples are not observed directly, but are instead observed by a relay (``teacher'') that transmits information through a memoryless channel to the decoder (``student''), who…

The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…

Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…

This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…

Variance is a ubiquitous quantity in quantum information theory. Given a basis, we consider the averaged variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the pure state and call…

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…

In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…

For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…

We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…

Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…

In empirical studies, the data usually don't include all the variables of interest in an economic model. This paper shows the identification of unobserved variables in observations at the population level. When the observables are distinct…

Doubly robust estimators have gained popularity in the field of causal inference due to their ability to provide consistent point estimates when either an outcome or exposure model is correctly specified. However, for nonrandomized…

The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…

Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…

The block bootstrap approximates sampling distributions from dependent data by resampling data blocks. A fundamental problem is establishing its consistency for the distribution of a sample mean, as a prototypical statistic. We use a…

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…