Related papers: A constructive proof of Simpson's Rule
We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of…
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
We put forward a proof of Solomon's rule, in terms of matrices, for multiplication in the descent algebra of the symmetric group. Our proof exploits the graphs that we can obtain from all the subsets of the set of transpositions,…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.
We first give a combinatorial proof of Stanley's shuffle theorem by using the insertion lemma of Haglund, Loehr and Remmel. Based on this combinatorial construction, we establish several refinements of Stanley's shuffle theorem.
This paper proves the approximate intermediate value theorem, constructively and from notably weak hypotheses: from pointwise rather than uniform continuity, without assuming that reals are presented with rational approximants, and without…
Student's theorem is an important result in statistics which states that for normal population, the sample variance is independent from the sample mean and has a chi-square distribution. The existing proofs of this theorem either overly…
The theory of symmetric multivariate Lagrange interpolation is a beautiful but rather unknown tool that has many applications. Here we derive from it an Exchange Lemma that allows to explain in a simple and natural way the full description…
The construction of modified equations is an important step in the backward error analysis of symplectic integrator for Hamiltonian systems. In the context of partial differential equations, the standard construction leads to modified…
A sum rule is an identity connecting the entropy of a measure with coefficients involved in the construction of its orthogonal polynomials (Jacobi coefficients). Our paper is an extension of Gamboa, Nagel and Rouault (2016), where we have…
The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…
This paper examines the concept of a combination rule for belief functions. It is shown that two fairly simple and apparently reasonable assumptions determine Dempster's rule, giving a new justification for it.
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…
This paper shows that sequential statistical analysis techniques can be generalised to the problem of selecting between alternative forecasting methods using scoring rules. A return to basic principles is necessary in order to show that…
In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result is an interpolation theorem.
The ordinary continued fractions expansion of a real number is based on the Euclidean division. Variants of the latter yield variants of the former, all encompassed by a more general Dynamical Systems framework. For all these variants the…
We construct a model of expert prediction where predictions can influence the state of the world. Under this model, we show through theoretical and numerical results that proper scoring rules can incentivize experts to manipulate the world…
Scoring rules are an important tool for evaluating the performance of probabilistic forecasting schemes. In the binary case, scoring rules (which are strictly proper) allow for a decomposition into terms related to the resolution and to the…
Prime numbers play a key role in number theory and have applications beyond Mathematics. In particular, in the Theory of Codes and also in Cryptography, the properties of prime numbers are relevant, because, from them, it is possible to…