Weak convergence for the row sums of a triangular array of empirical processes indexed by a manageable triangular array of functions
TLDR
In this article, the authors studied the weak convergence for the row sums of a general triangular array of empirical processes indexed by a manageable class of functions converging to an arbitrary limit.Abstract:
We study the weak convergence for the row sums of a general triangular array of empirical processes indexed by a manageable class of functions converging to an arbitrary limit. As particular cases, we consider random series processes and normalized sums of i.i.d. random processes with Gaussian and stable limits. An application to linear regression is presented. In this application, the limit of the row sum of a triangular array of empirical process is the mixture of a Gaussian process with a random series process.read more
Citations
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Asymptotic distribution of regression M-estimators
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The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes
TL;DR: In this paper, the authors studied the compact law of the iterated logarithm for a certain type of triangular arrays of empirical processes, appearing in statistics (M-estimators, regression, density estimation, etc).
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On the asymptotic accuracy of the bootstrap under arbitrary resampling size
TL;DR: In this paper, the authors study the order of convergence of the Kolmogorov-Smirnov distance for the bootstrap of the mean and the quantiles when an arbitrary bootstrap sample size is used.
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M-Estimators Converging to a Stable Limit
TL;DR: In this paper, the asymptotic linearization of multivariate M-estimators is studied when the limit distribution is stable, and weak conditions for the normality of M-stimators over differentiable kernels are given.
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Convergence of the Optimal M-Estimator over a Parametric Family of M-Estimators
TL;DR: In this paper, a method to select an optimal estimator over a family of M-estimators of a parameter was proposed. But it is not shown that this estimator is asymptotically normal under regularity conditions.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
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On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
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Convergence of stochastic processes
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