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Nonparametric Regression Estimation with Incomplete Data: Minimax Global Convergence Rates and Adaptivity
Adaptivity Besov spaces inhomogeneous data minimax estimation
2011/7/6
We consider the nonparametric regression estimation problem of recovering an unknown response function $f$ on the basis of incomplete data when the design points follow a known density $g$ with a fini...
Convergence rates in the strong law of large numbers for sums of random variables with multidimensional indices
Convergence rates random variables with multidimensional indices
2009/9/23
Convergence rates in the strong law of large numbers for sums of random variables with multidimensional indices。
A note on convergence rates in the strong law for strong mixing sequences
convergence rates the strong law for strong mixing sequences
2009/9/22
For partial sums {S,) of a stationary ergodic sequence
{X,} with zero mean we find conditions for
m
ny-'Pr {sup (S Jk) > E ] < m
n= 1 k?n
in terms of the strong mixing weficients {a,,) and moment...
Convergence rates in the strong law for associated random variables
Convergence rates in the strong law associated random variables
2009/9/22
We prove the Marcinkiewicz-Zygmund SLLN (MZ-
-SLLN) of order p, ~ � 1 12,[ , br associated sequences, not necessarily
stationary. Our assumption on the moment of the random variables is
minimal. We...
CONVERGENCE RATES IN THE LAW OF LARGE NUMBERS FOR ARRAYS
Arrays of rowwise independent random variables complete convergence
2009/9/18
In this paper we present new suficient conditions for
complete convergence for $urns of arrays of rowwise independent random
variables. These conditions appear to be necessary and sufficient
in the...
FINITE DIFFERENCE EQUATIONS AND CONVERGENCE RATES IN THE CENTRAL LIMIT THEOREM
Finite difference equations central limit theorem convergence rate interpolation theory
2009/9/18
We apply the theory of finite difference equations to
the central limit theorem, using interpolation of Banach spaces and
Fourier multipliers. Let S,T be a normalized sum of i.i.d. random vectors,
...
Quantitative Convergence Rates of Markov Chains: A Simple Account
Markov chain convergence rate mixing time drift condition minorisation condition total variation distance
2009/4/29
We state and prove a simple quantitative bound on the total variation distance after k iterations between two Markov chains with different initial distributions but identical transition probabilities....