Related papers: A few properties of sample variance
In this paper, by using the representation theorem for sublinear expectations, we give a simple proof to obtain two inequalities about the sample mean for independent random vectors under sublinear expectations.
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were…
Let $F=F_N$ be the distribution of a finite real population of size $N$. Let $\widehat{F}=F_N$ be the empirical distribution of a sample of size $n$ drawn from the population without replacement. We prove the following remarkable {\it…
Standard practice obtains an unbiased variance estimator by dividing by $N-1$ rather than $N$. Yet if only half the data are used to compute the mean, dividing by $N$ can still yield an unbiased estimator. We show that an alternative mean…
We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of…
Linear mixed-effects models are widely used in analyzing repeated measures data, including clustered and longitudinal data, where inferences of both fixed effects and variance components are of importance. Unlike the fixed effect inference…
We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
When using dyadic data (i.e., data indexed by pairs of units), researchers typically assume a linear model, estimate it using Ordinary Least Squares and conduct inference using ``dyadic-robust" variance estimators. The latter assumes that…
We show first that there are intrinsic relationships among different conditions, old and recent, which lead to some general statements in both the Stieltjes and the Hamburger moment problems. Then we describe checkable conditions and prove…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables get asymptotically independent as the sample size increases.…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…