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Limit theorems for kernel density estimators under dependent samples
Kernel density estimator consistency convergence rate mixing rate
2013/6/14
In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated....
Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds
Concentration Inequalities Confidence Bands Density Estimators
2011/3/21
Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}...
Minimax properties of beta kernel density estimators
Beta Kernel Density Minimax estimation
2010/3/9
In this paper, we are interested in the study of beta kernel estimators from
an asymptotic minimax point of view. It is well known that beta kernel estimators
are—on the contrary of classical kernel...
Equivalent conditions for the consistency of nonparametric spline density estimators
Equivalent conditions the consistency of nonparametric spline density estimators
2009/9/23
We study the nonparametric spline density estimators of
probability density. The equivalence of weak convergence for L,-consistency
of one density and completely for L,-consistency of all
densities...