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We prove a formula for the evaluation of expectations containing a scalar function of a Gaussian random vector multiplied by a product of the random vector components, each one raised to a non-negative integer power. Some of the powers…
Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…
Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. In this paper we show that all experiments that aim to prove Bell's theorem do not actually achieve…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…
We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and…
In this paper we deal with the estimation of population variance of the study variable y using auxiliary information on variable x. A family of ratio and product-type estimators are proposed using suitable transformation on both random…
We state and prove a theorem on the partitioning of a randomly selected large population into stationary and non-stationary components by using a property of stationary population identity. Applications of this theorem for practical…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
In this paper, we state and prove a simple geometric interpretation of the degrees of freedom of a chi-square distribution. The general geometric idea goes back at least to Fisher in the 1920s, but the exact result does not appear to have…
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…
This paper suggests a generalized class of estimators for population mean of the qualitative study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of bias and mean square error of the…
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of K\'atai's orthogonality criterion.…
For the space of functions that can be approximated by linear chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.
In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. We define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is…
We study the problem, introduced by Qiao and Valiant, of learning from untrusted batches. Here, we assume $m$ users, all of whom have samples from some underlying distribution $p$ over $1, \ldots, n$. Each user sends a batch of $k$ i.i.d.…
We give a functional representation theorem for a class of real p-Banach algebras. This theorem is used to show that every p-homogeneous seminorm with square property on a real associative algebra is submultiplicative.
We introduce an (evolution) algebra identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. The basic properties of the algebra are studied. We prove that this algebra is commutative…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…
We extend the notion of mex, which is central in combinatorial number theory, to an arbitrary combinatorial structure, and we prove a general theorem to determine the generating function of the objects having fixed mex. We then study this…