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Central Limit Theorems revisited
Statistics & Probability Letters, 2000The authors prove four central limit theorems (CLT). The first CLT is for a triangular array of random elements taking values in a real separable Hilbert space, where the components of the array are row-wise independent and have finite second moments, the covariance operator of the row sum satisfies mild convergence requirements, and the array ...
Majumdar, Suman +2 more
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Central limit theorems of pedigrees
Journal of Mathematical Biology, 1978Two multivariate central limit theorems are proved for polygenic trait values over a pedigree or collection of pedigrees. These theorems presuppose Hardy-Weinberg and linkage equilibrium for all loci, absence of assortative mating and epistasis, and a small variance for each locus compared to the total variance over many loci.
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2008
At the end of the 17th century, the mathematician Abraham de Moivre first used the normal distribution as an approximation for the percentage of successes in a large number of experiments. Later on, Laplace generalized his results, but it took 20th century mathematics to give an exact and complete description of this subject. So let me now describe the
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At the end of the 17th century, the mathematician Abraham de Moivre first used the normal distribution as an approximation for the percentage of successes in a large number of experiments. Later on, Laplace generalized his results, but it took 20th century mathematics to give an exact and complete description of this subject. So let me now describe the
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Central Limit Theorem in the Functional Approach
IEEE Transactions on Signal Processing, 2013The central limit theorem is proved within the framework of the functional approach for signal analysis. In this framework,a signal is modeled as a single function of time rather than a stochastic process. Distribution function, expectation, and all the familiar probabilistic parameters are built starting from this single function of time by resorting ...
Dehay, Dominique +2 more
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Conditional Central Limit Theorem
Theory of Probability & Its Applications, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Functional Central Limit Theorems
2008Central limit theorems guarantee that the distributions of properly normalized sums of certain random variables are approximately normal. In many cases, however, a more detailed analysis is necessary. When testing for structural constancy in models, we might be interested in the temporal evolution of our sums.
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A Counterexample in the Central Limit Theorem
Bulletin of the London Mathematical Society, 1999We construct a \(c_0\)-valued random variable \(X\) such that \((S_n/\sqrt{n})_{n\in N}\) has a convergent subsequence, but \(X\) does not satisfy the central limit theorem (CLT), thus give a counterexample against the subsequence rule in CLT.
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1981
Here we present some non-trivial limit theorems where the limit is a non-Gaussian self-similar field. The results of the previous chapters may explain at a heuristic level why such results should hold. But a rigorous proof demands much extra work whose consequences may be interesting in themselves.
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Here we present some non-trivial limit theorems where the limit is a non-Gaussian self-similar field. The results of the previous chapters may explain at a heuristic level why such results should hold. But a rigorous proof demands much extra work whose consequences may be interesting in themselves.
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Central Limit Theorems for Aggregate Efficiency
Operations Research, 2018Applied researchers in the field of efficiency and productivity analysis often need to estimate and make inference about aggregate efficiency, such as industry efficiency or aggregate efficiency of a group of distinct firms within an industry (e.g., public versus private firms, regulated versus unregulated firms, etc.).
Léopold Simar, Valentin Zelenyuk
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On the universal A.S. central limit theorem
Acta Mathematica Hungarica, 2007Let \(X_1 ,X_2 ,\dots\) be independent random variables such that for some measurable functions \(g_l \) the weak limit theorem \(g_l (X_1 ,\dots,X_l ) \Rightarrow G\) holds with some distribution function \(G\). The paper gives conditions for the validity of relation \(D_N^{ - 1} \sum\limits_{k = 1}^N {d_k f(g_k (X_1 ,\dots,X_k ))} =\int_{ - \infty }^\
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