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Showing 1 to 16 of 16 for “"Central Limit Theorems"”.
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Algebraic central limit theorems in noncommutative probability
… sufficient conditions for the existence of central limit laws. In contrast to classical probability theory, there exist many different central limit laws for exchangeable sequences of noncommutative random variables and still little is known about their concrete form. This thesis goes one …
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Central limit theorems for D[0,1]-valued random variables
Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics.
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LAWS OF LARGE NUMBERS AND CENTRAL LIMIT THEOREMS FOR RANDOM GEOMETRIC MEASURES. A COMPUTATIONAL APPROACH
… produce computational experiments related to a Central Limit Theorem (CLT) for random measures proved by Penrose in [4]. In particular we analyze some random measures associated with a segment process, a Voronoi tessellation and a Johnson-Mehl tessellation constructed on an underlying …
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Transport methods and universality for [beta]-ensembles
… regimes. In a different direction, we also prove Central Limit Theorems for the linear statistics of [beta]-ensembles at the macroscopic and mesoscopic scales.
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Sampling From Stratified Spaces
<p>This dissertation studies Central Limit Theorems (CLTs) of Frechet means on stratified spaces. The broad goal of this work is to answer the following question: What information one should expect to get by sampling from a stratified space? In particular, this work explores relationships between …
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On non-stationary Wishart matrices and functional Gaussian approximations in Hilbert spaces
… in the Wasserstein distance for the cases of central convergence and non-central convergence, verify such convergences hold in the weak topology of C([a; b]; M_n(R)), and show that our result can be used to prove convergence in expectation of the empirical spectral distributions of the Wishart …
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Applications of Stein's method and large deviations principle's in mean-field O(N) models
… graph in the mean-field (infinite-vertex) limit. Using theory of large deviations and Stein's method, in particular, Cramér and Sanov-type results, we present a number of results coming from the limit theorems with rates of convergence, and phase transition behavior for classical XY model. …
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PROBABILISTIC MODELS FOR DEPENDENT VARIABLES: COMPLEX ANALYTIC AND COMBINATORIAL APPROACHES
… parts. In the first part, we establish central limit theorems (CLTs) under zero-free conditions, building upon a quantitative extension of Marcinkiewicz's Theorem. In particular, we obtain quantitative decay estimates for the Kolmogorov-Smirnov distance between a real-valued random …
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Essays on Cross-Sectional and Network Dependence
… the kernel functions. Conditions are derived for central limit theorems to hold as corollaries. Chapter 2: We apply the limiting distribution theory for degenerate U-statistics, discussed in the previous chapter, to kernel smoothing based nonparametric specification tests, allowing for …
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On Variable Bandwidth Kernel Density And Regression Estimation
… density estimator. Furthermore, we present the central limit theorem of the true variable bandwidth kernel density estimator. We also propose a new variable bandwidth kernel regression estimator and estimate the bias and propose the central limit theorems for its ideal and true versions. For the …
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Two-Dimensional Discrete Gaussian Model at High Temperature
… in the delocalised phase, thereby obtaining central limit theorems in long-distance limit—in physics literature, the renormalisation group is a standard apparatus used to study scaling phenomena, in particular computing critical exponents and proving scaling limits and universality. We study …
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Variance reduction techniques for estimating quantiles and value-at-risk
… representation. Then this was employed to prove central limit theorems (CLTs) and to obtain consistent estimators of the variances in the CLTs, which were used to construct confidence intervals. After the theoretical framework was established, explicit algorithms were presented to construct …
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Approximation of Quantiles of Rank Test Statistics Using Almost Sure Limit Theorems
… is derived from an almost sure version of the central limit theorem using the results of Berkes and Csaki (2001), and it estimates the quantiles of a test statistic using only the data. To date, LQE has been used in only a few applications. We extend the use of LQE to three widely analyzed …
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Efficient nonparametric inference for discretely observed compound Poisson processes
… Under mild assumptions, we prove Donsker theorems for both (i.e. functional central limit theorems with the uniform norm) and identify the limiting Gaussian processes. This allows us to conclude that our estimators are efficient, or optimal from an information theory point of view, and to …
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Infinitesimal Probability Theory with Amalgamation
… the corresponding operator-valued infinitesimal Central Limit Theorem. We establish formulas to obtain the operator-valued infinitesimal free (respectively Boolean, monotone) additive convolution. Furthermore, for the free case, we also provide the formula for the operator-valued infinitesimal …
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Some application of Malliavin calculus to SPDE and convergence of densities
Some applications of Malliavin calculus to stochastic partial differential equations (SPDEs) and to normal approximation theory are studied in this dissertation. In Chapter 3, a Feynman-Kac formula is established for a stochastic heat equation driven by Gaussian noise which is, with respect to …