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Han and Liu (2012) proposed a method named transelliptical component analysis (TCA) for conducting scale-invariant principal component analysis on high dimensional data with transelliptical distributi...
For copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube, the empirical copula process does not converge weakly with respect to the supremum distance. This ...
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appear...
The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shi...
Majority vote plays a fundamental role in many applications of statistics, such as ensemble classifiers, crowdsourcing, and elections. When using majority vote as a prediction rule, it is of basic int...
Recently, it was demonstrated in [CS2012,CS2013] that the robustness of the classical Non-Local Means (NLM) algorithm [BCM2005] can be improved by incorporating $\ell^p (0 < p \leq 2)$ regression into...
The AdaBoost algorithm was designed to combine many "weak" hypotheses that perform slightly better than random guessing into a "strong" hypothesis that has very low error.
Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models.
It is shown the almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case. In this generalization, the step incr...
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distance...
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hy...
In this paper, we introduce the notion of efficiency (consistency) and examine some asymptotic properties of Markov chain Monte Carlo methods. We apply these results to the Gibbs sampler for independe...
We propose an extension of quasi-Newton methods, and investigate the convergence and the robustness properties of the proposed update formulae for the approximate Hessian matrix. Fletcher has studied ...
Following Hartigan [1975], a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering a...
The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the indepen- dence assumption is crucial...

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