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A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance
convex optimization minimax theorem robust optimization
2015/7/9
This paper concerns a fractional function of the form x^Ta/sqrt{x^TBx}, where B is positive definite. We consider the game of choosing x from a convex set, to maximize the function, and choosing (a,B)...
A New Proof of Convergence of MCMC via the Ergodic Theorem
Markov chain Monte Carlo Harris recurrence η-irreducibility
2015/7/6
A key result underlying the theory of MCMC is that any η-irreducible Markov chain having a transition density with respect to η and possessing a stationary distribution is automatically positive Harri...
A limit theorem for scaled eigenvectors of random dot product graphs
limit theorem scaled eigenvectors random dot product graphs
2013/6/14
We prove a central limit theorem for the components of the largest eigenvector of the adjacency matrix of a one-dimensional random dot product graph whose true latent positions are unknown. In particu...
A General Bernstein--von Mises Theorem in semiparametric models
A General Bernstein von Mises Theorem semiparametric models
2013/6/14
A Bernstein-von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems, in i.i.d. and non-i.i.d. situations. In particular, new ...
A uniform central limit theorem and efficiency for deconvolution estimators
Deconvolution Donsker theorem Efficiency Distribution function Smoothed empirical processes Fourier multiplier
2012/9/17
We estimate linear functionals in the classical deconvolution problem by kernel esti-mators. We obtain a uniform central limit theorem with √n–rate on the assumption that the smoothness of the functio...
Bell’s (1964) theorem is popularly supposed to establish the non-locality of quantum physics as a mathematical-physical theory. Building from this, observed violation of Bell’s inequality in experimen...
A central limit theorem for adaptive and interacting Markov chains
MCMC interacting MCMC Limit theorems
2011/7/19
Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distributions.
A continuous mapping theorem for the smallest argmax functional
continuous mapping smallest argmax d-dimensional Skorohod space
2011/6/16
This paper introduces a version of the argmax continuous mapping theorem that applies
to M-estimation problems in which the objective functions converge to a limiting process with
multiple maximizer...
In the so called lightbulb process, on days r = 1, . . . , n, out of n lightbulbs, all initially off, exactly rbulbs, selected uniformly and independent of the past, have their status changed from off...
Non-Central Limit Theorem Statistical Analysis for the “Long-tailed” Internet Society
Web 2.0 long tail statistics central limit theorem on-linecommunities text taggin
2010/3/10
This article presents a statistical analysis method and intro-
duces the corresponding software package ”tailstat,” which
is believed to be widely applicable to today’s internet so-
ciety. The prop...
A functional limit theorem for partial sums of dependent random variables with infinite variance
convergence in distribution functional limit the-orem GARCH mixing moving average partial sum point processes reg-ular variation
2010/3/9
Under an appropriate regular variation condition, the affinely
normalized partial sums of a sequence of independent and identically dis-
tributed random variables converges weakly to a non-Gaussian ...
Two members of an exponential family can be
represented as two points in the natural parameter space of that
family or as two points in the expectation parameter space. The
theorem describes a simp...
Central Limit Theorem in D for breakdown processes
Central Limit Theorem breakdown processes
2009/9/24
Central Limit Theorem in D for breakdown processes。
On the convergence rate in the central limit theorem of some functions of the average of independent random variables
the convergence rate the central limit theorem independent random variables
2009/9/24
This note gives the convergence rate in the central
limit theorem and the random central limit theorem of some
functions of the average of independent random variables.
On the central limit theorem in Banach space c (o)
the central limit theorem Banach space c (o)
2009/9/24
On the central limit theorem in Banach space c (o)。