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The Hausdorff distance between a compact convex set K CRd and random sets
K c lRd iS studied. Basic inequalities are derived for the case of K being a convex
subset of K. If applied to special seq...
On rates of convergence in the Curie-Weiss-Potts model with external field
rates of convergence Curie-Weiss-Potts model external field
2010/11/8
Stein's Method provides a way of bounding the distance of a probability distribution to a target distribution. In the present paper we obtain rates of convergence for limit theorems via Stein's Metho...
The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation
Berry–Esseen inequalities central limit theorem
2010/12/8
In Dolera, Gabetta and Regazzini [Ann. Appl. Probab. 19 (2009)186–201] it is proved that the total variation distance between the solution f(·, t) of Kac’s equation and the Gaussian density (0,2) has...
OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION
Nonparametric regression optimal rate o
2007/12/17
Let (X, Y) be a pair of random variables such that X ranges over [0, 1] and Y is real-valued and let go(X) be the conditional expectation of Y given X. Based on a training sample, the piecewise polyno...
Minimax Optimal Rates of Convergence for Multicategory Classifications
rate of convergence error probability modulus of continuity multicategory classification
2007/12/10
In the problem of
classification (or pattern recognition), given a set of $n$
samples, we attempt to construct a classifier $g_n$ with a small
misclassification error. It is important to study the ...