A Central Limit Theorem for incomplete U-statistics over triangular arrays

A central limit theorem for triangular arrays of weakly dependent random variables

We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi (1999). The proof uses an apparently new variant of the Lindeberg method where the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applicati...

Statistics 100 B Instructor : Nicolas Christou The Central Limit Theorem

The central limit theorem states that the sample mean X̄ follows approximately the normal distribution with mean μ and standard deviation σ √ n , where μ and σ are the mean and standard deviation of the population from where the sample was selected. The sample size n has to be large (usually n ≥ 30) if the population from where the sample is taken is nonnormal. If the population follows the norm...

Generalized Central Limit Theorem and Extreme Value Statistics

Central limit theorem: the cornerstone of modern statistics

According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-par...

Almost sure limit theorems for U-statistics

We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki (2001). We extend this result to the case of convergence to stable laws and also prove a functional version.