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Weak Convergence and Empirical Processes With Applications to Statistics
This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The...
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Weighted weak convergence of the sequential tail empirical process for heteroscedastic time series with an application to extreme value index estimation
The sequential tail empirical process is analyzed in a stochastic model allowing for serially dependent observations and heteroscedasticity of...
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A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity
In this paper, we estimate the high-dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the...
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Point process convergence for symmetric functions of high-dimensional random vectors
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a...
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Convergence Analysis
In this chapter, we begin our formal analysis of the stochastic approximation scheme in...
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Convergence of Random Variables
In this chapter, we discuss sequences of random variables and their convergence. The central limit theorem, one of the most important and widely-used...
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Mixing convergence of LSE for supercritical AR(2) processes with Gaussian innovations using random scaling
We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with...
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How to Improve MCMC Convergence
When modeling real-world data, MCMC may have poor convergence, which will make the calculation speed of sampling very slow. Poor convergence is...
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Mean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chains
This paper provides sets of sufficient conditions for mean convergence theorems for arrays of dependent random variables. We expand and improve a...
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On the convergence of Shannon entropy of distribution functions in the max domain of attraction of max-stable laws
We show that the convergence of the Shannon entropy of the probability density function of the normalized maxima of iid random variables to the...
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Probabilistic learning constrained by realizations using a weak formulation of Fourier transform of probability measures
This paper deals with the taking into account a given target set of realizations as constraints in the Kullback–Leibler divergence minimum principle...
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Convergence Rates of Attractive-Repulsive MCMC Algorithms
We consider MCMC algorithms for certain particle systems which include both attractive and repulsive forces, making their convergence analysis...
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Estimating weak periodic vector autoregressive time series
This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodic vector autoregressive time...
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A procedure for testing the hypothesis of weak efficiency in financial markets: a Monte Carlo simulation
The weak form of the efficient market hypothesis is identified with the conditions established by different types of random walks (1–3) on the...
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Improvements on SCORE, Especially for Weak Signals
A network may have weak signals and severe degree heterogeneity, and may be very sparse in one occurrence but very dense in another. SCORE (Ann....
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On the Asymptotic Behavior of the Leading Eigenvector of Tyler’s Shape Estimator Under Weak Identifiability
We consider point estimation in an elliptical Principal Component Analysis framework. More precisely, we focus on the problem of estimating the...